Is the first number divisible by the second? Use prime factorisation. Class 6

Is the first number divisible by the second? Use prime factorisation. Class 6

Question 1.

Is the first number divisible by the second? Use prime factorisation. Class 6

(a) 225 and 27

(b) 96 and 24

(c) 343 and 17

(d) 999 and 99

Solution:

(a) 225 = 3 × 3 × 5 × 5 and 27 = 3 × 3 × 3.

Since 3 occurs twice in 225 and 3 occurs three times in 27, so 225 is not divisible by 27.

(b) 96 = 2 × 2 × 2 × 2 × 2 × 3 and 24 = 2 × 2 × 2 × 3.

Since all the prime factors of 24 are included in the prime factors of 96, so 96 is divisible by 24.

(c) 343 = 7 × 7 × 7 and 17 = 17. Thus, 17 is not included in the prime factors of 343. So, 343 is not divisible by 17.

(d) 999 = 3 × 3 × 3 × 37 and 99 = 3 × 3 × 11.

Since prime factor 11 of 99 is not included

in the prime factors of 999, so 999 is not divisible by 99.

Question 2.

The first number has prime factorisation 2 × 3 × 7 and the second number has prime factorisation 3 × 7 × 11. Class 6

Are they co-prime? Does one of them divide the other?

Solution:

There are two prime factors 3 and 7 common in the two numbers. So, they are not co-prime.

Since all prime factors of one of these numbers are nlot included in the prime factors of the other number, so, one of them does not divide the other.