Question

Question 40

In the given question, state whether the given statement is True or False.

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

Answer 1

True
Given, a is divisible by b.
Let $b=p_1.p_2$, where $p_{1}and{p}_2$ are primes.
Since, a is divisible by b, a is a multiple of b
i.e. a = mb
$\Rightarrow$ a = m . $p_1.p_2$
or $a=c{p}_2=d{p}_1,$ where $c=m{p}_1,d=m{p}_2$
$\Rightarrow$ a is a multiple of $p_1$ as well as $p_2$.
Hence, a is divisible by each factor b.