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Question
If a number a is divisible by b, then it must be divisible by each factor of b.
Options
True
False
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Solution
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.
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