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

By Ritesh|Updated : November 7th, 2022

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.

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:

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

An amount can be divided by both 5 and 12. It will always divide evenly into 60. The various properties of numbers are reflexive property, zero product property, inverse multiplication, additive inverse, identity property, closure property, distributive property, etc.

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