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Divisible by 3, 6 and 9

bettermarks »Math book» Numbers »Divisibility and prime numbers» Divisibility rules »Divisibility by 3, 6 and 9

In these explanations you will learn how to check whether a number is divisible by 3, 6, or 9.

Divisibility rules for 3 and 6

The divisibility of a natural number by 3 is checked with its checksum. You calculate the cross sum by adding all the digits of the number. If the cross sum of a number is divisible by 3, then the number is divisible by 3, otherwise not. A number is divisible by 6 if it is divisible by 2 and by 3 (2 ∙ 3 ​​= 6), otherwise not. If the cross sum of a number is divisible by 3 and the number is even, then the number is divisible by 6.
Rule of divisibility for 3: A number is divisible by 3 if its checksum, i.e. the sum of its digits, is divisible by 3.
Divisibility rule for 6: A number is divisible by 6 if it is divisible by 2 and 3.
12561 is divisible by 3.
1256 is not divisible by 3.
3474 is divisible by 6.
3475 is not divisible by 6.
3478 is not divisible by 6.

Divisibility rule for 9

The divisibility of a natural number by 9 is checked with its cross sum. If the cross sum of a number is divisible by 9, then the number is divisible by 9, otherwise not.
Divisibility rule for 9: A number is divisible by 9 if its checksum, i.e. the sum of its digits, is divisible by 9, otherwise not.
12564 is divisible by 9.
12562 is not divisible by 9.