A number is divisible by both 5 and 12. By which another number will that number be always divisible?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

A number is divisible by both 5 and 12. It will always be divisible by 60. Considering that a number can be divided by both 5 and 12, The other number that the provided integer is always divisible by must be found. Knowing this:

Factors of 5 are 1, 5
Factors of 12 are 1, 2, 3, 4, 6, 12

Since 5 and 12 shares just one common factor, they are co-primes. We know that if a number is divisible by two co-primes, it is also divisible by the product of those two co-primes.

The product of 5 and 12 = 5 x 12 = 60.
The number can thus never be less than 60.

Table of content

1. A number is divisible by both 5 and 12. By which another number will that number be always divisible?

Properties of Numbers

Commutative Property: In accordance with the commutative property, if a and b are two real numbers;

a+b = b+a
a.b = b.a

In accordance with the associative property, if a, b, and c are three real numbers;

(a+b)+c = a+(b+c)
(a.b).c = a.(b.c)

Distributive Property: In accordance with distributive property, if a, b, and c are three real numbers;

a × (b + c) = a×b + a×c

Closure Property: If two numbers are combined together, just another number will result, like in;

a+b = c; where a, b and c are three real numbers.

Identity Property: A number will not change if we multiply it by one or by zero.

a+0=a
a.1 =a

Additive Inverse: If a number is added to another number that is negative in comparison, the outcome is zero.

a+(-a) = 0

Inverse multiplication: If a value other than 0 is multiplied by its own reciprocal, the outcome is 1.

a x (1/a) = 1

Zero Product Property: If a.b = 0, then; either a = 0 or b = 0.

Reflexive Property: This property reflects the number itself.

a = a

As a result, a number will be divisible by 60 if it is divisible by both 5 and 12.

Summary: