Students can practice TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Ex 3.2 to get the best methods of solving problems.
TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Exercise 3.2
Question 1.
Write all the factors of the following numbers.
(i) 36
Answer:
The factors of 36 are
1, 2, 3, 4, 6, 9, 12, 18, 36.
(ii) 23
Answer:
The factors of 23 are 1 and 23.
(iii) 96
Answer:
The factors of 96 are
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
(iv) 115
Answer:
The factors of 115 are 1, 5, 23, 115
Question 2.
Which of the following pairs are co-prime ?
(i) 16 and 35
Answer:
The factors of 18 are 1, 2, 3, 6, 9, 18.
The factors of 35 are 1, 5, 7, 35.
The common factor for both 18 and 35 is 1 only.
∴ 18 and 35 are co-primes.
(ii) 216 and 215
Answer:
The factors of 216 are 1,2,3,4,9,24, 36, 54, 72, 108,216.
The factors of 215 are 1, 5, 43.
The common factor for both 216 and 215 is 1 only.
∴ 216 and 215 are co-primes.
(iii) 30 and 415
Answer:
The factors for 30 are
1, 2, 3, 5, 6, 10, 15, 30.
The factors for 415 are 1, 5, 83.
The common factors for both 30 and 415 are 1, 5.
They have two common factors.
∴ 30 and 415 are not co-primes.
(iv) 17 and 68
Answer:
The factors for 17 are 1,17.
The factors for 68 are 1, 2, 4, 17, 34, 68.
The common factor for both 17 and 68 is 1 only.
∴ 17 and 68 are co-primes.
Question 3.
What is the greatest prime number between 1 and 20 ?
Answer:
The prime numbers between 1 and 20 are 2, 3,5, 7, 11,13, 17, 19.
∴ The greatest prime number is 19.
Question 4.
Find the prime ‘ and composite numbers between 10 and 30 ?
Answer:
The prime numbers between 10 and 30 are 11, 13, 17, 19, 23, 29.
The composite numbers between 10 and 30 are 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28.
Question 5.
The numbers 17 and 71 are prime numbers. Both these numbers have same digits 1 and 7. Find 2 more such pairs of prime numbers below 100.
Answer:
13 and 31; 37 and 73 are two pairs of prime numbers.
Question 6.
Write three pairs of twin primes below 20?
Answer:
(3, 5); (5, 7); (11, 13) are twin primes.
Question 7.
Write two prime numbers whose product is 35.
Answer:
The two prime numbers whose product is 35 are 5 and 7.
Question 8.
Express 36 as the sum of two odd primes.
Answer:
The two odd primes whose sum is 36 are 13 and 23.
∴ 36 = 13 + 23
Question 9.
Write seven consecutive composite numbers less than 100.
Answer:
4, 6, 8, 10, 12, 14 and 16
Question 10.
Express 53 as the sum of three primes.
Answer:
53 = 3 + 19 + 31
Question 11.
Write two prime numbers whose difference is 10.
Answer:
19 and 29. (∵ 29 – 19 = 10)
Question 12.
Write three pairs of prime numbers less than 20 whose sum is divisible by 5?
Answer:
(3, 7), (7, 13), (17, 3)
These pairs of prime numbers are less than 20. The sum of each pair is divisible by 5.