Divisible by 3
A number is divisible by 3, if the sum of its all digits is a multiple of 3 or divisibility by 3.
Consider the multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, .........
|
Number |
Sum of the Digits |
|
12 15 18 21 24 27 |
1 + 2 = 3 1 + 5 = 6 1 + 8 = 9 2 + 1 = 3 2 + 4 = 6 2 + 7 = 9 |
In each case the sum of the digits is divisible by 3.
A number is divisible by 3 if the sum of its digits is divisible by 3.
1. Let us consider the following numbers to find whether the numbers are divisible or not divisible by 3:
(i) 54
Sum of all the digits of 54 = 5 + 4 = 9, which is divisible by 3.
Hence, 54 is divisible by 3.
(ii) 73
Sum of all the digits of 73 = 7 + 3 = 10, which is not divisible by 3.
Hence, 73 is not divisible by 3.
(iii) 137
Sum of all the digits of 137 = 1 + 3 + 7 = 11, which is not divisible by 3.
Hence, 137 is not divisible by 3.
(iv) 231
Sum of all the digits of 231 = 2 + 3 + 1 = 6, which is divisible by 3.
Hence, 231 is divisible by 3.
(v) 194
Sum of all the digits of 194 = 1 + 9 + 4 = 14, which is not divisible by 3.
Hence, 194 is not divisible by 3.
(vi) 153
Sum of all the digits of 153 = 1 + 5 + 3 = 9, which is divisible by 3.
Hence, 54 is divisible by 3.
(vii) 171
Sum of all the digits of 171 = 1 + 7 + 1 = 9, which is divisible by 3.
Hence, 171 is divisible by 3.
(viii) 277
Sum of all the digits of 277 = 2 + 7 + 7 = 16, which is not divisible by 3.
Hence, 277 is not divisible by 3.
(ix) 276
Sum of all the digits of 276 = 2 + 7 + 6 = 15, which is divisible by 3.
Hence, 276 is divisible by 3.
(x) 179
Sum of all the digits of 179 = 1 + 7 + 9 = 17, which is not divisible by 3.
Hence, 179 is not divisible by 3.
2. Is 756 divisible by 3?
7 + 5 + 6 = 18 (18 is a multiple of 3)
Hence 756 is divisible by 3
We can verify that 756 is divisible by 3 by actual division.
3. In the number 46 * 8782, replace * by (i) a smallest digit and (ii) a largest digit to make it divisible by 3.
Solution:
The sum of the digits in the number 46 * 8782 = 4 + 6+ 8 + 7 + 8 + 2 = 35
(i) The number next to 35 which is divisible by 3 = 36.
Therefore, * is to be replaced by 1 i.e., 36 - 35 = 1;
Hence, the smallest digit 1 replaces * so as to make the number 4618782 divisible by 3.
(ii) We know that 35 + 7 = 42, which is divisible by 3.
Hence, the required largest digit 7 replaces * so as to make the number 4678782 divisible by 3.
Worksheet on Divisible by 3:
1. Fill the correct lowest possible digit in the blank space to make the number divisible by 3.
(i) 16335_
(ii) 20_984
(iii) 8422_1
(iv) 749_261
(v) 999_32
(vi) 1_7073
Answer:
1. (i) 3
(ii) 4
(iii) 1
(iv) 1
(v) 1
(vi) 3
2. Which of the following numbers are divisible by 3?
(i) 875
(ii) 729
(iii) 3647
(iv) 8504
(v) 111
(vi) 3732
(vii) 6425
(viii) 963
Answer:
2. (ii) 729
(v) 111
(vi) 3732
(viii) 963
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