Ques 1: Fill up the blanks:
(i) Write all even prime numbers __________.
Ans: 2
The only even prime number is 2. Other even numbers are divisible by 2 and hence not prime.
(ii) Number of factors of 2 are __________.
Ans: two (1 and 2)
Factors of a number are the numbers that divide it without leaving a remainder. For 2, the factors are 1 and 2.
(iii) Smallest pair of coprime numbers is __________.
Ans: (2, 1)
Coprime numbers are numbers that have no common factors other than 1. The smallest pair is (2, 1).
(iv) Smallest twin prime numbers are __________.
Ans: 3, 5
Twin prime numbers are prime numbers that have a difference of 2 between them. The smallest twin primes are 3 and 5.
(v) The largest 2digit number which is odd and prime is __________.
Ans: 97
Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. 97 is the largest prime number within the range of 2digit odd numbers.
Ques 2: Find the smallest number which is divisible by 2, 3, 4, and 5. Can we find the largest number which is divisible by 2, 3, 4 and 5?
Ans: 60, No
The smallest number divisible by 2, 3, 4, and 5 is their least common multiple (LCM), which is 60. No, we cannot find the largest number divisible by 2, 3, 4, and 5 because there is no upper limit to the set of numbers divisible by those factors.
Ques 3: Write the smallest 3digit number which is exactly divisible by 6.
Ans: The smallest 3digit number divisible by 6 is 102.
Ques 4: Replace '*' by the smallest possible digit so that the following numbers are divisible by 3 and 9:
(i) *4129
Ans: 2
4129: The smallest digit to replace * so that the number is divisible by both 3 and 9 is 2.
(ii) 2*985
Ans: 3
2985: The smallest digit to replace * so that the number is divisible by both 3 and 9 is 3.
(iii) 987*32
Ans: 7
987*32: The smallest digit to replace * so that the number is divisible by both 3 and 9 is 7.
Ques 5: Write the largest 3digit number which is divisible by 11.
Ans: The largest 3digit number divisible by 11 is 990.
Ques 6: Find HCF of 15 m 60 cm and 20 m 16 cm.
Ans: The highest common factor (HCF) of the lengths 15 m 60 cm and 20 m 16 cm is 24 cm.
Ques 7: Find the least number which when divided by 25, 40 and 60 leave the remainder 7 in each case.
Ans: The least number that satisfies this condition is 607.
Ques 8: Find HCF of 90 and 243. Check if it divides 90 and 243 both.
Ans: The HCF of 90 and 243 is 9, and yes, it divides both 90 and 243.
Ques 9: Find LCM of 18 and 15. Check if the LCM so obtained is divisible by 15 as well as 18.
Ans: The least common multiple (LCM) of 18 and 15 is 90, and yes, it is divisible by both 15 and 18.
Ques 10: Match the following:
(i) HCF of two consecutive numbers  (a) 4 
(ii) LCM of two coprime numbers  (b) 97 
(iii) HCF of two consecutive even numbers  (c) 1 
(iv) Smallest composite number  (d) 2 
(v) Largest 2digit prime number  (e) product of two numbers 
Ans. (i) ↔ (c)
(ii) ↔ (e)
(iii) ↔ (d)
(iv) ↔ (a)
(v) ↔ (b)
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1. What are some common strategies for playing with numbers? 
2. How can playing with numbers improve mathematical skills? 
3. Are there any online resources available for practicing number games and puzzles? 
4. Can playing with numbers help in reallife applications outside of mathematics? 
5. How can parents and educators incorporate number games into children's learning and development? 

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