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.

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Solution

True
Given, a is divisible by b.
Let $b = p_{1} . p_{2}$ , where $p_{1} a n d p_{2}$ 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.

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Divisibility Tests

Standard VI Mathematics

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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.

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.

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.