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.
Questions and Answers 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
Problems on Divisibility Rules
Worksheet on Divisibility Rules
5th Grade Math Problems
From Divisible by 3 to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Apr 24, 24 03:46 PM
Apr 24, 24 03:45 PM
Apr 24, 24 03:35 PM
Apr 24, 24 02:57 PM
Apr 24, 24 12:38 PM