If a number a is divisible by b,
Question:

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

Solution:

True

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.

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