Playing with Numbers- 2 Class 6 Worksheet Maths

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 co-prime numbers is __________.

Ans: (2, 1)

Co-prime 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 2-digit 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 2-digit 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 3-digit number which is exactly divisible by 6.
Ans: The smallest 3-digit 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 3-digit number which is divisible by 11.
Ans: The largest 3-digit 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:

Ans. (i) ↔ (c)
(ii) ↔ (e)
(iii) ↔ (d)
(iv) ↔ (a)
(v) ↔ (b)