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.