3.6 Some More Divisibility Rules

Let us observe a few more rules about the divisibility of numbers.
(i) Can you give a factor of 18? It is 9. Name a factor of 9? It is 3. Is 3 a factor of 18? Yes it is. Take any other factor of 18, say 6. Now, 2 is a factor of 6 and it also divides 18. Check this for the other factors of 18. Consider 24. It is divisible by 8 and the factors of 8 i.e. 1, 2, 4 and 8 also divide 24.

So, we may say that if a number is divisible by another number then it is divisible by each of the factors of that number.

(ii) The number 80 is divisible by 4 and 5. It is also divisible by 4 × 5 = 20, and 4 and 5 are co-primes.

Similarly, 60 is divisible by 3 and 5 which are co-primes. 60 is also divisible by 3 × 5 = 15.

If a number is divisible by two co-prime numbers then it is divisible by their product also.

(iii) The numbers 16 and 20 are both divisible by 4. The number 16 + 20 = 36 is also divisible by 4. Check this for other pairs of numbers.

Try this for other common divisors of 16 and 20.

If two given numbers are divisible by a number, then their sum is also divisible by that number.

(iv) The numbers 35 and 20 are both divisible by 5. Is their difference 35 − 20 = 15 also divisible by 5 ? Try this for other pairs of numbers also.

If two given numbers are divisible by a number, then their difference is also divisible by that number.

Take different pairs of numbers and check the four rules given above.