Divisibility by 12

Divisibility Test

Divisibility tests, often known as division rules in Maths, are used to see if a number is divisible by another integer without having to utilise the division method. If a number is completely divisible by another integer, the quotient will be a whole number and the remainder will be zero. A nonzero integer m divides an integer n if there is an integer q such that n=mq. To state that m is a divisor of n and that m is a factor of n, we use the notation m|n.

General Properties of Divisibility

Property 1: If a number is divisible by another number, it must also be divisible by each of its factors.

Example We already know that 36 may be divided by 12.

All 12 components are 1, 2, 3, 4, 6, and 12.

Property 2: If a number is divisible by each of two co-prime integers, it must also be divisible by the product of those numbers.

Example We know that 972 is divisible by each one of the numbers 2 and 3. Also, 2 and 3 are co-primes.

Property 3: If a number is a factor of both the supplied numbers, it must also be a factor of their sum.

Example We know that 5 is a factor of 15 as well as that of 20. So, 5 must be a factor of (15+20), that is 35. And, this is clear. 

Property 4: If a number is a factor of both the given numbers, it must also be a factor of the difference between them.

Example We know that 3 is a factor of each one of the numbers 36 and 24. So, 3 must be a factor of (36-24) = 12. Clearly, 3 divides 12 exactly.

Test of Divisibility by 12

To see if an integer is divisible by 12, apply the Divisibility Rule for 12. It’s also known as the divisibility test for 12. If the sum of the digits in a number is divisible by 3 and the number’s last two digits are divisible by 4, the number is divisible by 12. Remember both the conditions should be met for the number to be divisible by 12. One more rule by which it can be determined that a number is divisible by 12, is that we subtract the last digit from twice the rest. Numbers like 1608, 36, 108 are divisible by 12. 

Conclusion 

In this article, we learnt about the divisibility test of 12. It says that if a number to is divisible by 12 it should be divisible by 3 and 4. For divisibility of 4, the last two digits of the number should be divisible and for divisibility of 3, we add the values of the digits if the result comes out to be divisible by 3.