# What Are the Divisibility Rules?

A number is said to be divisible by another number if the answer to the division is an integer. Divisibility is about which numbers can be divided by other numbers. For example, 6 is divisible by 2 because $6:2=3$.

There are rules about the divisibility of certain numbers. Here, I’ll show you how to tell if a number is divisible by 2, 3, 4, 5, 6, 9 and/or 10.

Rule

DIVIDING BY 2:

All even numbers are divisible by 2. Because of that, all numbers that end in 0, 2, 4, 6 and 8 are divisible by 2.

DIVIDING BY 3:

All numbers where the sum of the digits is divisible by 3 are also divisible by 3 themselves.

DIVIDING BY 4:

All numbers where the number made up of the last two digits is divisible by 4 are also divisible by 4.

DIVIDING BY 5:

All numbers that end with 0 or 5 are divisible by 5.

DIVIDING BY 6:

All numbers that fulfill both DIVIDING BY 2 and DIVIDING BY 3 are divisible by 6.

DIVIDING BY 9:

All numbers where the sum of the digits is divisible by 9 are also divisible by 9.

DIVIDING BY 10:

All numbers that end with 0 are divisible by 10.

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It’s important to remember that all numbers has 1 as a factor. All numbers are divisible by themselves, and the answer to that division is always 1.

Example 1

Is the number 234 divisible by 2, 3, 4, 5, 6, 9 or 10?

You have to check if 234 fulfills any of the conditions above:

• Because 234 ends in an even number, it is divisible by 2.

• Because $2+3+4=9$, and 9 is divisible by 3, 234 is also divisible by 3.

• Because $34÷4=8.5$, and $8.5$ isn’t an integer, 234 is not divisible by 4.

• As 234 doesn’t end in 0 or 5, it’s not divisible by 5.

• Because 234 is divisible by both 2 and 3, it’s also divisible by 6.

• Because $2+3+4=9$, and 9 is divisible by 9, 234 is also divisible by 9.

• As 234 doesn’t end with 0, it’s not divisible by 10.

Example 2

Use the numbers 2, 3 and 5 to make numbers with three digits that are divisible by either 2, 3, or 5

Numbers that are divisible by 2 have to end with an even number. The only even number we have access to is 2, so the only possible numbers are the ones that end with 2:

$\begin{array}{cc}532\phantom{\rule{1em}{0ex}}352\phantom{\rule{1em}{0ex}}222\phantom{\rule{1em}{0ex}}332\phantom{\rule{1em}{0ex}}552& \\ 252\phantom{\rule{1em}{0ex}}232\phantom{\rule{1em}{0ex}}522\phantom{\rule{1em}{0ex}}322& \end{array}$

For numbers that are divisible by 3, the sum of the digits has to be divisible by 3. That makes these the possible numbers:

$\begin{array}{cc}522\phantom{\rule{1em}{0ex}}252\phantom{\rule{1em}{0ex}}225\phantom{\rule{1em}{0ex}}552\phantom{\rule{1em}{0ex}}525& \\ 255\phantom{\rule{1em}{0ex}}222\phantom{\rule{1em}{0ex}}333\phantom{\rule{1em}{0ex}}555.& \end{array}$

For a number to be divisible by 5, it has to end with 0 or 5. The possible numbers are then

$\begin{array}{cc}225\phantom{\rule{1em}{0ex}}235\phantom{\rule{1em}{0ex}}335\phantom{\rule{1em}{0ex}}325\phantom{\rule{1em}{0ex}}555& \\ 525\phantom{\rule{1em}{0ex}}535\phantom{\rule{1em}{0ex}}255\phantom{\rule{1em}{0ex}}355.& \end{array}$