A number is divisible by 12 if it's divisible by both 3 and 4. This is because 12 = 3 x 4, and if a number is divisible by both factors, it must also be divisible by their product.
Checking for Divisibility by 3:
To determine if a number is divisible by 3, add all its digits. If the sum is divisible by 3, then the original number is also divisible by 3.
- Example: Consider the number 132. 1 + 3 + 2 = 6. Since 6 is divisible by 3, 132 is divisible by 3.
Checking for Divisibility by 4:
A number is divisible by 4 if its last two digits form a number divisible by 4.
- Example: Consider the number 132 again. The last two digits are "32". Since 32 is divisible by 4 (32/4 = 8), 132 is divisible by 4.
Combining the Tests:
Since 132 is divisible by both 3 and 4, it's divisible by 12 (132 / 12 = 11).
Practical Application and Further Insights:
This two-step process provides a quick way to check divisibility by 12 without performing the actual division. This method is based on the fundamental theorem of arithmetic, which states that every integer greater than 1 can be represented uniquely as a product of prime numbers. Since 12 = 2 x 2 x 3, checking divisibility by 3 and 4 covers all prime factors of 12. Note that checking for divisibility by 2 and 6 will not suffice, because 2 and 6 share a common factor (2).
As noted in multiple sources like Smartick, Byju's, and various Quora answers, this combined approach is the most efficient way to determine divisibility by 12. The YouTube video "Divisibility Rule for 12 | Math with Mr. J" ([YouTube Link Placeholder]) further reinforces this concept.
