# Number System : Divisibility by 4

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The basic rule for divisibility by 4 is that if the number formed by the last two digits in a number is divisible by 4, the original number is divisible by 4; this is because 100 is divisible by 4 and so adding hundreds, thousands, etc. is simply adding another number that is divisible by 4. If any number ends in a two digit number that you know is divisible by 4 (e.g. 24, 04, 08, etc.), then the whole number will be

divisible by 4 regardless of what is before the last two digits.

Alternatively, one can simply divide the number by 2, and then check the result to find if it is divisible by 2. If it is, the original number is divisible by 4. In addition, the result of this test is the same as the original number divided by 4.

**Example**

**General rule**

- 1096 (This is the original number)
- 10 96 (Take only the last two digits of the number)
- 96 ÷ 4 = 24 (Check if the number is divisible by 4)
- 1096 ÷ 4 = 274 (If the last two digit is divisible by 4, then the original number is divisible by 4)

**Alternative example**

- 5324 (This is the original number)
- 5324 ÷ 2 = 2662 (Divide the original number by 2)
- 2662 ÷ 2 = 1331 (Check to see if the result obtained is divisible by 2)
- 5324 ÷ 4 = 1331 (If the result is divisible by 2, then the original number is divisible by 4)
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