Question

If a number a is divisible by b, then it must be divisible by each factor of b.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Given, a is divisible by b.

Let b = p₁ × p₂, where p₁ and p₂ are primes.

Since, a is divisible by b, a is a multiple of b

i.e. a = mb

⇒ a = m(p₁)(p₂)

or a = cp₂ = dp₁, where c = mp₁, d = mp₂

⇒ a is a multiple of p₁ as well as p₂.

Hence, a is divisible by each factor b.