# Divisible by 9

This rule states that a number is divisible by 9 if the sum of its digits of the number is divisible by 9

For Example: Check whether 729 is divisible by 9 or not?

Sum of the digits = 7 + 2 + 9 = 18

Now 18 is divisible by 9 hence, 729 is also divisible by 9

Here are few examples illustrated on the divisibility rule of 9

1. Check whether the following number is divisible by 9 or not?

(i) 9729

(ii) 5256

(iii) 8852

(iv) 2136

(v) 4086

(vi) 5103

(vii) 8811

(viii) 813

(ix) 891

(x) 45363

Solution:

(i) 9729

Sum of the digits = 9 + 7 + 2 + 9 = 27

As, 27 is divisible by 9 hence, 9729 is also divisible by 9

(ii) 5256

Sum of the digits = 5 + 2 + 5 + 6 = 18

5256 is divisible by 9 as 18 is divisible by 9

(iii) 8852

Sum of the digits = 8 + 8 + 5 + 2 = 23

As, 23 is not divisible by 9 hence, 8852 is not divisible by 9

(iv) 2136

Sum of the digits = 2 + 1 + 3 + 6 = 12

As, 12 is not divisible by 9 hence, 2136 is not divisible by 9

(v) 4086

Sum of the digits = 4 + 0 + 8 + 6= 18

18 is divisible by 9 hence, 4086 is also divisible by 9

(vi) 5103

Sum of the digits = 5 + 1 + 0 + 3 = 9

As, 9 is divisible by 9 hence the number I divisible by 9

(vii) 8811

Sum of digits = 8 + 8 + 1 + 1 = 18

8811 is divisible by 9 as 18 is a multiple of 9

(viii) 813

Sum of the digits = 8 + 1 + 3= 12

813 is not divisible by as 12 is a multiple of 9

(ix) 891

Sum of the digits = 8 + 9 + 1 = 18

18 is a multiple of 9 hence, 891 is divisible by 9

(x) 45363

Sum of the digits = 4 + 5 + 3 + 6 + 3 = 21

As, 21 is not divisible by 9 hence, 45363 is not divisible by 9

2. Rewrite the series in a different color with numbers that are divisible by 9.

8581    7272    2345    9090    3027    981      3203    6580    6057

Solution:

8581    7272    2345    9090    3027    981      3203    6580    6057

3. Fill in the blanks with digits to make the following numbers divisible by 9:

(i) 7 … 96

(ii) 45 … 1

(iii) 10 … 3

(iv) 9 … 56

(v) 7 … 11

(vi) 4 … 23

(vii) 125 …

(viii) … 525

(ix) 332 …

(x) 556 …

Solution:

(i) 7596

(ii) 4581

(iii) 1053

(iv) 9756

(v) 7011

(vi) 4023

(vii) 1251

(viii) 6525

(ix) 3321

(x) 5562

Note: In the above example fill in with such digit so as to make the sum of the digits divisible by 9

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