Page 154 - Ganit Kaushal

Ex 25. Which of the following statements are True or False?

(a) If a number is divisible by 3, it must be divisible by 9.
(b) If a number is divisible by 9, it must be divisible by 3.

(c) A number is divisible by 18 if it is divisible by both 3 and 6.
(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.
(e) If two numbers are co-prime, at least one of them must be prime.

Sol. (a) False [ 12 is divisible by 3 but not by 9]
(b) True [ 3 is a factor of 9]

(c) False [ 12 is divisible by both 3 and 6, but not by 18]
(d) True [ 9, 10 are co-prime]
(e) False [ 9, 10 are co-prime, but neither of them is prime]

Exercise 5.3

1. Using prime factorisation, check if 242 and 195 are co-prime or not. (NCERT)
2. Using prime factorisation, check the divisibility of 75 by 21. (NCERT)
3. Find the prime factorisation of the following numbers:

(a) 64 (b) 104 (c) 105 (d) 243
4. Find the prime factorisation of (108 × 75) without actually multiplying them.

5. Are the following pairs of numbers co-prime? Use prime factorisation to verify your answer.
(a) 121 and 1331 (b) 343 and 216 (NCERT)
6. Is the first number divisible by the second? Use prime factorisation.

(a) 184 and 46 (b) 190 and 24
7. Which of the following numbers are divisible by all of 2, 4, 5, 8 and 10:
572, 2352, 5600, 6000, 77622160. (NCERT)

8. Use the division algorithm to find the remainder when 99 is divided by 10, 5, and 2, respectively.
9. Fill the grid with prime numbers only, so that the product of each row is the number 105
to the right of the row and the product of each column is the number below the 20
column. (NCERT) 30
28 125 18
10. Write the greatest 4-digit number and express it in terms of its prime factors. Also,
make its factor tree.
11. Which of the following statements are True or False?

(a) All numbers which are divisible by 4 must also be divisible by 8.
(b) All numbers which are divisible by 8 must also be divisible by 4.
(c) If a number exactly divides two numbers separately, it must exactly divide their sum.

(d) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers
separately.

152 Mathematics-6