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All questions of Prime Factors, HCF & LCM for Class 10 Exam
The LCM of two number is 84. Which one of the following can’t be their HCF.- a)6
- b)8
- c)21
- d)24
Correct answer is option 'B'. Can you explain this answer?
The LCM of two number is 84. Which one of the following can’t be their HCF.
a)
6
b)
8
c)
21
d)
24
|
Aditi Sharma answered |
LCM is divisible by HCF.
Hence, 8 cannot be the HCF because 84 is not divisible by 8.
Which of these are co-prime
(a) 16,18
(b) 11,48
(c) 8,23- a)b and c
- b)b
- c)a
- d)a and c
Correct answer is option 'A'. Can you explain this answer?
Which of these are co-prime
(a) 16,18
(b) 11,48
(c) 8,23
(a) 16,18
(b) 11,48
(c) 8,23
a)
b and c
b)
b
c)
a
d)
a and c
|
|
Aditi Sharma answered |
In number theory, Co-prime numbers are those numbers if the only positive factor that divides them is 1.
Here,
Option A: (16,18) Factors that divide both of them are 1,2.
Option B: (11,48) Factor that divides both of them is 1.
Option C: (8,23) Factor that divides both of them is 1.
In reference to above definition both b and c are co-prime numbers.
5695 is divisible by- a)2
- b)3
- c)4
- d)5
Correct answer is option 'D'. Can you explain this answer?
5695 is divisible by
a)
2
b)
3
c)
4
d)
5
|
Priyanka Sharma answered |
The last digits of any number must end with 0 or 5 to be divisible by 5.
The last digit of 5695 is 5.
Therefore, 5695 is divisible by 5.
The last digit of 5695 is 5.
Therefore, 5695 is divisible by 5.
The HCF of two numbers is 9. Which one can’t be their LCM?- a)24
- b)36
- c)54
- d)48
Correct answer is option 'D'. Can you explain this answer?
The HCF of two numbers is 9. Which one can’t be their LCM?
a)
24
b)
36
c)
54
d)
48
|
|
Avinash Patel answered |
H.C.F of two numbers is the highest factor present in both the numbers.
So we can say, if the HCF of two numbers is 9 then the two numbers can be 9x and 9y where x and y are co-prime.
The LCM of these two numbers = product of these two numbers.
So, LCM of 9x and 9y = 9xy (Only one 9 in the LCM because it is a common factor of both the numbers).
Hence, we can conclude that the LCM must be an integral multiple of 9 as x and y are integers.
From the options given only 48 is the number which is not an integral multiple of 9. So it can never be the LCM.
HCF of 190, 171 and 152 is- a)20
- b)19
- c)18
- d)17
Correct answer is option 'B'. Can you explain this answer?
HCF of 190, 171 and 152 is
a)
20
b)
19
c)
18
d)
17
|
|
Priyanka Sharma answered |
190 = 2 x 5 x 19
152 = 2 x 2 x 2 x 19
171 = 3 x 3 x 19
The common factor of the numbers is 19.
Hence, the HCF of 190 , 152 , 171 is 19.
4, 6, 8, 9, 10, 12 are _______- a)even numbers
- b)prime numbers
- c)composite numbers
- d)none of the above
Correct answer is option 'C'. Can you explain this answer?
4, 6, 8, 9, 10, 12 are _______
a)
even numbers
b)
prime numbers
c)
composite numbers
d)
none of the above
|
|
Aditi Sharma answered |
- Composite numbers are numbers with more than two factors.
- 4, 6, 8, 9, 10, 12 have more than two factors, hence they are composite numbers.
LCM of 3, 4 and 5 is- a)60
- b)30
- c)20
- d)40
Correct answer is option 'A'. Can you explain this answer?
LCM of 3, 4 and 5 is
a)
60
b)
30
c)
20
d)
40
|
|
Avinash Patel answered |
The value of LCM(3, 4, 5) will be the smallest number that is exactly divisible by 3, 4, and 5.
Multiples of 3, 4, and 5:
Multiples of 3, 4, and 5:
- Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . ., 48, 51, 54, 57, 60, . . . .
- Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, . . . ., 52, 56, 60, . . . .
- Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . . ., 45, 50, 55, 60, . . . .
Therefore, the LCM of 3, 4, and 5 is 60.
3, 7, 9, 11, 13 are- a)even numbers
- b)odd numbers
- c)prime numbers
- d)none of the above
Correct answer is option 'B'. Can you explain this answer?
3, 7, 9, 11, 13 are
a)
even numbers
b)
odd numbers
c)
prime numbers
d)
none of the above
|
|
Priyanka Sharma answered |
- Odd numbers are whole numbers that cannot be divided exactly into pairs.
- 3, 7, 9, 11, 13 cannot be divided into pairs, hence they are odd numbers.
The LCM of two co- prime number is 176. If one number is 16, find the other number.- a)22
- b)33
- c)11
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
The LCM of two co- prime number is 176. If one number is 16, find the other number.
a)
22
b)
33
c)
11
d)
None of the above
|
|
Priyanka Sharma answered |
The product of 2 co-prime numbers is equal to their LCM.
Hence, if one number is 16 other one is
HCF of co-prime no. is always- a)3
- b)1
- c)2
- d)0
Correct answer is option 'B'. Can you explain this answer?
HCF of co-prime no. is always
a)
3
b)
1
c)
2
d)
0
|
|
Avinash Patel answered |
- The HCF of two coprime numbers is always 1.
- For example, 5 and 9 are coprime numbers, there, HCF (5, 9) = 1.
The HCF of two numbers is 6 and their LCM is 144. If one of the numbers is 36, the other is- a)26
- b)24
- c)22
- d)28
Correct answer is option 'B'. Can you explain this answer?
The HCF of two numbers is 6 and their LCM is 144. If one of the numbers is 36, the other is
a)
26
b)
24
c)
22
d)
28
|
|
Priyanka Sharma answered |
Let the other number be x
Product of two numbers = HCF × LCM
x × 36 = 6 × 144
Hence, the other number is x = 24
Among the biotic components of the ecosystem the producer system is - a) Cow
- b) Peacock
- c) Tiger
- d) Green plants
Correct answer is option 'D'. Can you explain this answer?
Among the biotic components of the ecosystem the producer system is
a)
Cow
b)
Peacock
c)
Tiger
d)
Green plants
|
Deepa Iyer answered |
Green plants act as producers in the ecosystem. Due to the process of photosynthesis, green plants produce their food and also known as autotrophs. Animals are categorized as consumers in the ecosystem and are dependent upon producers for nutrients.
Chapter doubts & questions for Prime Factors, HCF & LCM - Mathematics for GCSE/IGCSE 2025 is part of Class 10 exam preparation. The chapters have been prepared according to the Class 10 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 10 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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