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Page 1 Chapter 9: HCF-LCM PRACTICE SET 23 [PAGE 46] Practice Set 23 | Q 1 | Page 46 Write all the factor of the given number and list their common factor. 12, 16 SOLUTION Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 16: 1, 2, 4, 8, 16 Common factors of 12 and 16: 1, 2, 4 Practice Set 23 | Q 2 | Page 46 Write all the factor of the given number and list their common factor. 21, 24 SOLUTION Factors of 21: 1, 3, 7, 21 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Common factors of 21 and 24: 1, 3 Practice Set 23 | Q 3 | Page 46 Write all the factor of the given number and list their common factor. 25, 30 SOLUTION Factors of 25: 1, 5, 25 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Common factors of 25 and 30: 1, 5 Practice Set 23 | Q 4 | Page 46 Write all the factor of the given number and list their common factor. 24, 25 SOLUTION Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 25: 1, 5, 25 Common factors of 24 and 25: 1 Page 2 Chapter 9: HCF-LCM PRACTICE SET 23 [PAGE 46] Practice Set 23 | Q 1 | Page 46 Write all the factor of the given number and list their common factor. 12, 16 SOLUTION Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 16: 1, 2, 4, 8, 16 Common factors of 12 and 16: 1, 2, 4 Practice Set 23 | Q 2 | Page 46 Write all the factor of the given number and list their common factor. 21, 24 SOLUTION Factors of 21: 1, 3, 7, 21 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Common factors of 21 and 24: 1, 3 Practice Set 23 | Q 3 | Page 46 Write all the factor of the given number and list their common factor. 25, 30 SOLUTION Factors of 25: 1, 5, 25 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Common factors of 25 and 30: 1, 5 Practice Set 23 | Q 4 | Page 46 Write all the factor of the given number and list their common factor. 24, 25 SOLUTION Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 25: 1, 5, 25 Common factors of 24 and 25: 1 Practice Set 23 | Q 5 | Page 46 Write all the factor of the given number and list their common factor. 56, 72 SOLUTION Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Common factors of 56 and 72: 1, 2, 4, 8 PRACTICE SET 24 [PAGE 47] Practice Set 24 | Q 1.01 | Page 47 Find the HCF of the following number. 45, 30 SOLUTION Factors of 45: 1, 3, 5, 9, 15, 45 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Common factors of 45 and 30: 1, 3, 5, 15 ? HCF of 45 and 30 = 15 Practice Set 24 | Q 1.02 | Page 47 Find the HCF of the following number. 16, 48 SOLUTION Factors of 16: 1, 2, 4, 8, 16 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Common factors of 16 and 48: 1, 2, 4, 8, 16 ? HCF of 16 and 48 = 16 Practice Set 24 | Q 1.03 | Page 47 Find the HCF of the following number. 39, 25 SOLUTION Factors of 39: 1, 3, 13, 39 Page 3 Chapter 9: HCF-LCM PRACTICE SET 23 [PAGE 46] Practice Set 23 | Q 1 | Page 46 Write all the factor of the given number and list their common factor. 12, 16 SOLUTION Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 16: 1, 2, 4, 8, 16 Common factors of 12 and 16: 1, 2, 4 Practice Set 23 | Q 2 | Page 46 Write all the factor of the given number and list their common factor. 21, 24 SOLUTION Factors of 21: 1, 3, 7, 21 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Common factors of 21 and 24: 1, 3 Practice Set 23 | Q 3 | Page 46 Write all the factor of the given number and list their common factor. 25, 30 SOLUTION Factors of 25: 1, 5, 25 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Common factors of 25 and 30: 1, 5 Practice Set 23 | Q 4 | Page 46 Write all the factor of the given number and list their common factor. 24, 25 SOLUTION Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 25: 1, 5, 25 Common factors of 24 and 25: 1 Practice Set 23 | Q 5 | Page 46 Write all the factor of the given number and list their common factor. 56, 72 SOLUTION Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Common factors of 56 and 72: 1, 2, 4, 8 PRACTICE SET 24 [PAGE 47] Practice Set 24 | Q 1.01 | Page 47 Find the HCF of the following number. 45, 30 SOLUTION Factors of 45: 1, 3, 5, 9, 15, 45 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Common factors of 45 and 30: 1, 3, 5, 15 ? HCF of 45 and 30 = 15 Practice Set 24 | Q 1.02 | Page 47 Find the HCF of the following number. 16, 48 SOLUTION Factors of 16: 1, 2, 4, 8, 16 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Common factors of 16 and 48: 1, 2, 4, 8, 16 ? HCF of 16 and 48 = 16 Practice Set 24 | Q 1.03 | Page 47 Find the HCF of the following number. 39, 25 SOLUTION Factors of 39: 1, 3, 13, 39 Factors of 25: 1, 5, 25 Common factors of 39 and 25: 1 ? HCF of 39 and 25 = 1 Practice Set 24 | Q 1.04 | Page 47 Find the HCF of the following number. 49, 56 SOLUTION Factors of 49: 1, 7, 49 Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 Common factors of 49 and 56: 1, 7 ? HCF of 49 and 56 = 7 Practice Set 24 | Q 1.05 | Page 47 Find the HCF of the following number. 120, 144 SOLUTION Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 Common factors of 120 and 144: 1, 2, 3, 4, 6, 8, 12, 24 ? HCF of 120 and 144 = 24 Practice Set 24 | Q 1.06 | Page 47 Find the HCF of the following number. 81, 99 SOLUTION Factors of 81: 1, 3, 9, 27, 81 Factors of 99: 1, 3, 9, 11, 33, 99 Common factors of 81 and 99: 1, 3, 9 ? HCF of 81 and 99 = 9 Practice Set 24 | Q 1.07 | Page 47 Find the HCF of the following number. 24, 36 SOLUTION Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Page 4 Chapter 9: HCF-LCM PRACTICE SET 23 [PAGE 46] Practice Set 23 | Q 1 | Page 46 Write all the factor of the given number and list their common factor. 12, 16 SOLUTION Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 16: 1, 2, 4, 8, 16 Common factors of 12 and 16: 1, 2, 4 Practice Set 23 | Q 2 | Page 46 Write all the factor of the given number and list their common factor. 21, 24 SOLUTION Factors of 21: 1, 3, 7, 21 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Common factors of 21 and 24: 1, 3 Practice Set 23 | Q 3 | Page 46 Write all the factor of the given number and list their common factor. 25, 30 SOLUTION Factors of 25: 1, 5, 25 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Common factors of 25 and 30: 1, 5 Practice Set 23 | Q 4 | Page 46 Write all the factor of the given number and list their common factor. 24, 25 SOLUTION Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 25: 1, 5, 25 Common factors of 24 and 25: 1 Practice Set 23 | Q 5 | Page 46 Write all the factor of the given number and list their common factor. 56, 72 SOLUTION Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Common factors of 56 and 72: 1, 2, 4, 8 PRACTICE SET 24 [PAGE 47] Practice Set 24 | Q 1.01 | Page 47 Find the HCF of the following number. 45, 30 SOLUTION Factors of 45: 1, 3, 5, 9, 15, 45 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Common factors of 45 and 30: 1, 3, 5, 15 ? HCF of 45 and 30 = 15 Practice Set 24 | Q 1.02 | Page 47 Find the HCF of the following number. 16, 48 SOLUTION Factors of 16: 1, 2, 4, 8, 16 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Common factors of 16 and 48: 1, 2, 4, 8, 16 ? HCF of 16 and 48 = 16 Practice Set 24 | Q 1.03 | Page 47 Find the HCF of the following number. 39, 25 SOLUTION Factors of 39: 1, 3, 13, 39 Factors of 25: 1, 5, 25 Common factors of 39 and 25: 1 ? HCF of 39 and 25 = 1 Practice Set 24 | Q 1.04 | Page 47 Find the HCF of the following number. 49, 56 SOLUTION Factors of 49: 1, 7, 49 Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 Common factors of 49 and 56: 1, 7 ? HCF of 49 and 56 = 7 Practice Set 24 | Q 1.05 | Page 47 Find the HCF of the following number. 120, 144 SOLUTION Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 Common factors of 120 and 144: 1, 2, 3, 4, 6, 8, 12, 24 ? HCF of 120 and 144 = 24 Practice Set 24 | Q 1.06 | Page 47 Find the HCF of the following number. 81, 99 SOLUTION Factors of 81: 1, 3, 9, 27, 81 Factors of 99: 1, 3, 9, 11, 33, 99 Common factors of 81 and 99: 1, 3, 9 ? HCF of 81 and 99 = 9 Practice Set 24 | Q 1.07 | Page 47 Find the HCF of the following number. 24, 36 SOLUTION Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Common factors of 24 and 36: 1, 2, 3, 4, 6, 12 ? HCF of 24 and 36 = 12 Practice Set 24 | Q 1.08 | Page 47 Find the HCF of the following number. 25, 75 SOLUTION Factors of 25: 1, 5, 25 Factors of 75: 1, 3, 5, 15, 25, 75 Common factors of 25 and 75: 1, 5, 25 ? HCF of 25 and 75 = 25 Practice Set 24 | Q 1.09 | Page 47 Find the HCF of the following number. 48, 54 SOLUTION Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54 Common factors of 48 and 54: 1, 2, 3, 6 ? HCF of 48 and 54 = 6 Practice Set 24 | Q 1.10 | Page 47 Find the HCF of the following number. 150, 225 SOLUTION Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, 225 Common factors of 150 and 225: 1, 3, 5, 15, 25, 75 ? HCF of 150 and 225 = 75 Practice Set 24 | Q 2 | Page 47 If large square beds of equal size are to be made for planting vegetables on a plot of land 18 meters long and 15 meters wide, what is the maximum possible length of each bed? Page 5 Chapter 9: HCF-LCM PRACTICE SET 23 [PAGE 46] Practice Set 23 | Q 1 | Page 46 Write all the factor of the given number and list their common factor. 12, 16 SOLUTION Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 16: 1, 2, 4, 8, 16 Common factors of 12 and 16: 1, 2, 4 Practice Set 23 | Q 2 | Page 46 Write all the factor of the given number and list their common factor. 21, 24 SOLUTION Factors of 21: 1, 3, 7, 21 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Common factors of 21 and 24: 1, 3 Practice Set 23 | Q 3 | Page 46 Write all the factor of the given number and list their common factor. 25, 30 SOLUTION Factors of 25: 1, 5, 25 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Common factors of 25 and 30: 1, 5 Practice Set 23 | Q 4 | Page 46 Write all the factor of the given number and list their common factor. 24, 25 SOLUTION Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 25: 1, 5, 25 Common factors of 24 and 25: 1 Practice Set 23 | Q 5 | Page 46 Write all the factor of the given number and list their common factor. 56, 72 SOLUTION Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Common factors of 56 and 72: 1, 2, 4, 8 PRACTICE SET 24 [PAGE 47] Practice Set 24 | Q 1.01 | Page 47 Find the HCF of the following number. 45, 30 SOLUTION Factors of 45: 1, 3, 5, 9, 15, 45 Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 Common factors of 45 and 30: 1, 3, 5, 15 ? HCF of 45 and 30 = 15 Practice Set 24 | Q 1.02 | Page 47 Find the HCF of the following number. 16, 48 SOLUTION Factors of 16: 1, 2, 4, 8, 16 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Common factors of 16 and 48: 1, 2, 4, 8, 16 ? HCF of 16 and 48 = 16 Practice Set 24 | Q 1.03 | Page 47 Find the HCF of the following number. 39, 25 SOLUTION Factors of 39: 1, 3, 13, 39 Factors of 25: 1, 5, 25 Common factors of 39 and 25: 1 ? HCF of 39 and 25 = 1 Practice Set 24 | Q 1.04 | Page 47 Find the HCF of the following number. 49, 56 SOLUTION Factors of 49: 1, 7, 49 Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 Common factors of 49 and 56: 1, 7 ? HCF of 49 and 56 = 7 Practice Set 24 | Q 1.05 | Page 47 Find the HCF of the following number. 120, 144 SOLUTION Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 Common factors of 120 and 144: 1, 2, 3, 4, 6, 8, 12, 24 ? HCF of 120 and 144 = 24 Practice Set 24 | Q 1.06 | Page 47 Find the HCF of the following number. 81, 99 SOLUTION Factors of 81: 1, 3, 9, 27, 81 Factors of 99: 1, 3, 9, 11, 33, 99 Common factors of 81 and 99: 1, 3, 9 ? HCF of 81 and 99 = 9 Practice Set 24 | Q 1.07 | Page 47 Find the HCF of the following number. 24, 36 SOLUTION Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Common factors of 24 and 36: 1, 2, 3, 4, 6, 12 ? HCF of 24 and 36 = 12 Practice Set 24 | Q 1.08 | Page 47 Find the HCF of the following number. 25, 75 SOLUTION Factors of 25: 1, 5, 25 Factors of 75: 1, 3, 5, 15, 25, 75 Common factors of 25 and 75: 1, 5, 25 ? HCF of 25 and 75 = 25 Practice Set 24 | Q 1.09 | Page 47 Find the HCF of the following number. 48, 54 SOLUTION Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54 Common factors of 48 and 54: 1, 2, 3, 6 ? HCF of 48 and 54 = 6 Practice Set 24 | Q 1.10 | Page 47 Find the HCF of the following number. 150, 225 SOLUTION Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, 225 Common factors of 150 and 225: 1, 3, 5, 15, 25, 75 ? HCF of 150 and 225 = 75 Practice Set 24 | Q 2 | Page 47 If large square beds of equal size are to be made for planting vegetables on a plot of land 18 meters long and 15 meters wide, what is the maximum possible length of each bed? SOLUTION Length of the plot = 18 m Breadth of the plot = 15 m The maximum possible length of each square bed is the HCF of 18 m and 15 m. Factors of 18 = 1, 2, 3, 6, 9, 18 Factors of 15 = 1, 3, 5, 15 Common factors of 18 and 15 = 1, 3 HCF of 18 and 15 = 3 ? Maximum possible length of each square bed = 3 m Thus, the maximum possible length of each square bed is 3 m. Practice Set 24 | Q 3 | Page 47 Two ropes, one 8 meters long and the other 12 meters long are to be cut into pieces of the same length. What will the maximum possible length of each piece be? SOLUTION Length of one rope = 8 m Length of other rope = 12 m The maximum possible length of each piece of rope of the same length that can be cut from the two given ropes is the HCF of 8 m and 12 m. Factors of 8: 1, 2, 4, 8 Factors of 12: 1, 2, 3, 4, 6, 12 Common factors of 8 and 12: 1, 2, 4 HCF of 8 and 12 = 4 ? Maximum possible length of each piece of rope of same length = 4 m Thus, the maximum possible length of each piece of rope is 4 m. Practice Set 24 | Q 4 | Page 47 The number of students of Std 6th and Std 7th who went to visit the Tadoba Tiger Project at Chandrapur was 140 and 196 respectively. The students of each class are to be divided into groups of the same number of students. Each group can have a paid guide. What is the maximum number of students there can be in each group ? Why do you think each group should have the maximum possible number of students? SOLUTION Number of students of Std 6th = 140Read More
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FAQs on Textbook Solutions: HCF & LCM - Mathematics Class 6 (Maharashtra Board)
| 1. What is the difference between HCF and LCM? |  |
Ans. HCF, or Highest Common Factor, is the largest number that can divide two or more numbers without leaving a remainder. LCM, or Least Common Multiple, is the smallest number that is a multiple of two or more numbers. While HCF focuses on the factors that numbers share, LCM focuses on the multiples that numbers share.
| 2. How can we find the HCF of two numbers? | |
Ans. To find the HCF of two numbers, one common method is to list all the factors of each number and identify the largest factor they share. Alternatively, the prime factorization method can be used, where you break down each number into its prime factors and multiply the common prime factors together to find the HCF.
| 3. What are some real-life applications of HCF and LCM? | |
Ans. HCF and LCM have various real-life applications. HCF is often used in situations like dividing things into equal groups, such as sharing candies among friends. LCM is useful in scenarios involving scheduling, such as determining when two events will occur simultaneously, like two buses arriving at a station at the same time.
| 4. Can HCF and LCM be calculated for more than two numbers? | |
Ans. Yes, HCF and LCM can be calculated for more than two numbers. For HCF, you can find the HCF of the first two numbers and then find the HCF of that result with the next number, continuing this process. For LCM, you can find the LCM of the first two numbers and then find the LCM of that result with the next number, continuing in the same manner.
| 5. Is there a relationship between HCF and LCM of two numbers? | |
Ans. Yes, there is a relationship between HCF and LCM of two numbers. The product of the HCF and LCM of two numbers is equal to the product of the numbers themselves. This relationship can be expressed as: HCF(a, b) × LCM(a, b) = a × b. This principle helps in finding either the HCF or LCM if the other is known.
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