What is the divisibility rule of 6?

Answer 1

The number you want to test must be divisible by 2 and 3 both! Hence the divisibility rules for 2 and 3 both must be applicable to the number to be tested.

In short:

(i) It must be even and, at the same time

(ii) The digital sum of the number must also be divisible by 3.

Answer 2

Divisibility by:
2 If the last digit is even, the number is divisible by 2.

3 If the sum of the digits is divisible by 3, the number is also.

4 If the last two digits form a number divisible by 4, the number is also.

5 If the last digit is a 5 or a 0, the number is divisible by 5.

6 If the number is divisible by both 3 and 2, it is also divisible by 6.

7 Take the last digit, double it, and subtract it from the rest of the number;
if the answer is divisible by 7 (including 0), then the number is also.

8 If the last three digits form a number divisible by 8,
then so is the whole number.

9 If the sum of the digits is divisible by 9, the number is also.

10 If the number ends in 0, it is divisible by 10.

11 Alternately add and subtract the digits from left to right. (You can think of the first digit as being 'added' to zero.)
If the result (including 0) is divisible by 11, the number is also.
Example: to see whether 365167484 is divisible by 11, start by subtracting:
[0+]3-6+5-1+6-7+4-8+4 = 0; therefore 365167484 is divisible by 11.

12 If the number is divisible by both 3 and 4, it is also divisible by 12.

13 Delete the last digit from the number, then subtract 9 times the deleted
digit from the remaining number. If what is left is divisible by 13, then so is the original number.

Answer 3

A comment about ironduke's answer:

He's combined two rules to get a third one.

1. Even numbers are divisible by 2
2. If the sum of the digits is divisible by 3 then the number is divisible by 3

So you can see that if both of these are true then the number is divisible by both 2 and 3 hence their product 6.

Answer 4

Rule A number is divisible by 6 if it is even and if the sum of its digits is divisible by 3.

Answer 5

To determine if a number is prime or composite, follow these steps:
Find all factors of the number.
If the number has only two factors, 1 and itself, then it is prime.
If the number has more than two factors, then it is composite.


The above procedure works very well for small numbers. However, it would be time-consuming to find all factors of 621. Thus we need a better method for determining if a large number is prime or composite. Every number has one and itself as a factor. Thus, if we could find one factor of 621, other than 1 and itself, we could prove that 621 is composite. One way to find factors of large numbers quickly is to use tests for divisibility.

Definition Example
One whole number is divisible by another if, after dividing, the remainder is zero. 18 is divisible by 9 since 18 ÷ 9 = 2 with a remainder of 0.
If one whole number is divisible by another number, then the second number is a factor of the first number. Since 18 is divisible by 9, 9 is a factor of 18.
A divisibility test is a rule for determining whether one whole number is divisible by another. It is a quick way to find factors of large numbers. Divisibility Test for 3: if the sum of the digits of a number is divisible by 3, then the number is divisible by 3.



We can test for divisibility by 3 (see table above) to quickly find a factor of 621 other than 1 and itself. The sum of the digits of 621 is 6+2+1 = 9. This divisibility test and the definitions above tell us that...

621 is divisible by 3 since the sum of its digits (9) is divisible by 3.
Since 621 is divisible by 3, 3 is a factor of 621.
Since the factors of 621 include 1, 3 and 621, we have proven that 621 has more than two factors.
Since 621 has more than 2 factors, we have proven that it is composite.


Let's look at some other tests for divisibility and examples of each.

Divisibility Tests Example
A number is divisible by 2 if the last digit is 0, 2, 4, 6 or 8. 168 is divisible by 2 since the last digit is 8.
A number is divisible by 3 if the sum of the digits is divisible by 3. 168 is divisible by 3 since the sum of the digits is 15 (1+6+8=15), and 15 is divisible by 3.
A number is divisible by 4 if the number formed by the last two digits is divisible by 4. 316 is divisible by 4 since 16 is divisible by 4.
A number is divisible by 5 if the last digit is either 0 or 5. 195 is divisible by 5 since the last digit is 5.
A number is divisible by 6 if it is divisible by 2 AND it is divisible by 3. 168 is divisible by 6 since it is divisible by 2 AND it is divisible by 3.
A number is divisible by 8 if the number formed by the last three digits is divisible by 8. 7,120 is divisible by 8 since 120 is divisible by 8.
A number is divisible by 9 if the sum of the digits is divisible by 9. 549 is divisible by 9 since the sum of the digits is 18 (5+4+9=18), and 18 is divisible by 9.
A number is divisible by 10 if the last digit is 0. 1,470 is divisible by 10 since the last digit is 0.

Answer 6

boang