Divisible by 9

Divisible by 9 is discussed below:

Consider the multiples of 9: 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, .......

Number

Sum of the Digits

1 + 8 = 9

5 + 4 = 9

7 + 2 = 9

In each case it can be observed that the sum of the digits is divisible by 9.

A number is divisible by 9, if the sum is a multiple of 9 or if the sum of its digits is divisible by 9.

1. Consider the following numbers which are divisible by 9, using the test of divisibility by 9:

99, 198, 171, 9990, 3411.

(i) 99

Sum of the digits of 99 = 9 + 9 = 18, which is divisible by 9.

Hence, 99 is divisible by 9.

(ii) 198

Sum of the digits of 198 = 1 + 9 + 8 = 18, which is divisible by 9.

Hence, 198 is divisible by 9.

(iii) 171

Sum of the digits of 171 = 1 + 7 + 1 = 9, which is divisible by 9.

Hence, 171 is divisible by 9.

(iv) 9990

Sum of the digits of 9990 = 9 + 9 + 9+ 0 = 27, which is divisible by 9.

Hence, 9990 is divisible by 9.

(v) 3411

Sum of the digits of 3411 = 3 + 4 + 1+ 1 = 9, which is divisible by 9.

Hence, 3411 is divisible by 9.

2. Consider the following numbers which are not divisible by 9, using the rules of divisibility by 9:

73, 237, 394, 1277, 1379.

Note: A number is divisible by 9 if the sum of its digits is divisible by 9.

(i) 73

Sum of the digits of 73 = 7 + 3 = 10, which is not divisible by 9.

Hence, 73 is not divisible by 9.

(ii) 237

Sum of the digits of 237 = 2 + 3 + 7 = 12, which is not divisible by 9.

Hence, 237 is not divisible by 9.

(iii) 394

Sum of the digits of 394 = 3 + 9 + 4 = 16, which is not divisible by 9.

Hence, 394 is not divisible by 9.

(iv) 1277

Sum of the digits of 1277 = 1 + 2 + 7 + 7 = 17, which is not divisible by 9.

Hence, 1277 is not divisible by 9.

(v) 1379

Sum of the digits of 1379 = 1 + 3 + 7 + 9 = 20, which is not divisible by 9.

Hence, 1379 is not divisible by 9.

3. Is 5328 divisible by 9?

Solution:

Sum of its digits = 5 + 3 + 2 + 8 = 18, divisible by 9.

Hence 5328 is divisible by 9.

We can verify that 5328 is divisible by 9 by actual division.

Questions and Answers on Divisible by 9:

1. Choose the numbers which are divisible by 9.

13 27 128 65 730363 900 1375

Answer: 27, 900

2. Which of the following numbers are divisible by 9?

(i) 855

(ii) 97

(iii) 4830

(iv) 9189

(v) 8469

Answer:

2. (i) 855

(iv) 9189

(v) 8469

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