Divisibility by 24

Divisibility Test

Divisibility tests, often known as division rules in Math, are used to determine whether a number is divisible by another integer without using the division method. The quotient will be a whole number and the remainder will be zero if a number is totally divisible by another integer. If there is an integer q such that n=mq, a nonzero integer m divides an integer n. We use the notation m|n to express that m is a divisor of n and that m is a factor of n.

General Properties of Divisibility

Property1 If a number is divisible by another number, it must be divisible by each other of the factors of that number.

Example We know that 36 is divisible by 12.

All factors of 12 are 1, 2, 3, 4, 6, 12

Property2 If a number is divisible by each of two co-prime numbers, it must be divisible by their product.

Example We know that 4320 is divisible by each of the numbers 5 and 8. Also 5 and 8 co-primes. So 4320 must be divisible by 40. By long division, we find that it is true.

Property3 If a number is a factor of each of the two given numbers, then it must be a factor of their sum. 

Example We know that 7 is a factor of each of the numbers 49 and 63. So, 7 must be a factor of (49+63)=112. Clearly, 7 divides 112.

Property4 If a number is a factor of each of the two given numbers then it must be a factor of their difference.

Example We know that 13 is a factor of each one of the numbers 65 and 117. So, 13 must be a factor of (117-65)=52. Clearly, 13 divides 52 exactly.

Test of Divisibility by 24

For any number given to be divisible by 24, make sure the integer is divisible by three and eight.

If both integers are divisible by 24, the original number is also divisible by 24. For divisibility by 3, we add the values of all the digits in the number and if the resulting number is divisible by 3 the given number is divisible by 3. For divisibility by 8, we take the last 3 digits of the number and check if they are divisible by 8. If both these rules follow, the given original number is divisible by 24.

Conclusion

We learnt when a number is divisible by 24. A number is divisible by 24, when we check its divisibility by 3 and 8 and both should be true.