Page 46 - Revised Maths Wisdom Class - 6

44 MATHS

To make prime factorisation easy, we must learn divisibility rules. These rules once learned will help in elimination
of unnecessary calculations and save time. There is no need to perform actual division until asked for.

Divisibility Test
Divisors Rules for Divisibility Examples

2 A number is divisible by 2 if its ones place digits are 0, 2, 8234 is divisible by 2 as its ones place digit is 4.
4, 6 or 8.
3 A number is divisible by 3 if the sum of its digits is divisible 1635 is divisible by 3 as the sum of its digits 1 + 6
by 3. + 3 + 5 = 15 is divisible by 3.
4 A number is divisible by 4 if the number formed by its last 776 is divisible by 4 as number formed by last two
two digits i.e., tens and ones is divisible by 4. digits, i.e., 76 is divisible by 4.
5 A number is divisible by 5 if its ones place digit is 0 or 5. 18050 is divisible by 5 as its ones place digit is 0.
6 A number is divisible by 6 if it is divisible by 2 and 3 both. 7224 is divisible by 2 as its ones place is 4. It is
also divisible by 3 as 7 + 2 + 2 + 4 = 15 is divisible
by 3. Hence, 7224 is divisible by 6.

7 A number is divisible by 7 if the last digit is doubled and 357 is divisible by 7 as 7 × 2 = 14 and 35 – 14 = 21
subtracted from the rest of the number and the number is a multiple of 7.
obtained is 0 or multiple of 7.
8 A number is divisible by 8 if the number formed by the last 3096 is divisible by 8 as 096 is divisible by 8.
three digits, i.e., hundreds, tens and ones is divisible by 8.
9 A number is divisible by 9 if the sum of its digits is divisible 9252 is divisible by 9 as 9 + 2 + 5 + 2 = 18 is
by 9 divisible by 9.
10 A number is divisible by 10 if its ones place digit is 0. 1010 or 190 are divisible by 10 as their last digit is 0.

11 A number is divisible by 11 if the difference of the sum of 3729 is divisible by 11 as Sum of 3 + 2 = 5
digits at even places and sum of digits at odd places is 0 or Sum of 7 + 9 = 16
a multiple of 11. Difference = 16 – 5 = 11 is a multiple of 11.

12 A number is divisible by 12 if it is divisible by 3 and 4 both. 3816 is divisible by 12 as it is divisible by 3 and 4 both.

While the above stated rules are divisor specific there are few more divisibility rules that help us:

1. If a number is divisible by another number then it is divisible by each of the factors of that number.
For example, 42 = 7 × 6 thus 42 is divisible by 7 and 6 both,
Factors of 6 = 1, 2, 3, 6
Factors of 7 = 1, 7
So as per the rule 42 is divisible by 1, 2, 3, 6 and 7.

2. If a number is divisible by two co-prime numbers, then it is divisible by their product also.
For example, 715 is divisible by 11 and 13 also (11, 13) are co-primes. Now their product
= 11 × 13 = 143
Thus, 715 is divisible by 143 as 715 ÷ 143 = 5.

3. If two numbers are divisible by a number, then their sum is also divisible by that number.
For example, 85 and 68 are divisible by 17 then
85 + 68 = 153 is also divisible by 17 as 153 ÷ 17 = 9
4. If two numbers are divisible by a number, then their difference is also divisible by that number.
For example, 49 and 70 are divisible by 7, then 70 – 49 = 21 is also divisible by 7 as 21 ÷ 7 = 3.