A number is divisible by 4 if its last two digits form a number that is divisible by 4.
Understanding Divisibility by 4
The simplest way to determine if a number is divisible by 4 is to examine only its last two digits. If this two-digit number is divisible by 4 (meaning it leaves no remainder when divided by 4), then the entire number is also divisible by 4.
This rule is based on the place value system. Any number can be expressed as a sum of multiples of powers of 10. For example, the number 1236 can be written as (1000 x 1) + (200 x 1) + (30 x 1) + (6 x 1). Since 100 is divisible by 4 (100 = 4 x 25), any multiple of 100 is also divisible by 4. This means we only need to consider the last two digits when checking for divisibility by 4.
Examples
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Divisible by 4:
- 1236: The last two digits, 36, are divisible by 4 (36 ÷ 4 = 9). Therefore, 1236 is divisible by 4.
- 804: The last two digits, 4, are divisible by 4 (4 ÷ 4 = 1). Therefore, 804 is divisible by 4.
- 7800: The last two digits are 00, which is divisible by 4. Therefore 7800 is divisible by 4.
- 10204: The last two digits, 04, are divisible by 4 (4 ÷ 4 = 1). Therefore, 10204 is divisible by 4.
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Not Divisible by 4:
- 1235: The last two digits, 35, are not divisible by 4 (35 ÷ 4 = 8 with a remainder of 3). Therefore, 1235 is not divisible by 4.
- 9871: The last two digits, 71, are not divisible by 4 (71 ÷ 4 = 17 with a remainder of 3). Therefore, 9871 is not divisible by 4.
Practical Application
This divisibility rule is helpful for quickly checking if a number is divisible by 4 without performing long division. This is particularly useful in mental math calculations or estimations.
References Supporting the Rule
Multiple sources confirm this divisibility rule: Cuemath, SplashLearn, SparkNotes, Smartick, Byjus, Vedantu, and Grayson College all state that a number is divisible by 4 if its last two digits are divisible by 4.
