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Question

If a number 'x' is divisible by another number 'y', then 'x' is also divisible by all the prime factors of 'y'.


A

True

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B

False

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Solution

The correct option is A

True


Suppose x is divisible by y giving a quotient z.

xy= z

or x = y × z ............(1)
y can be written as a product of its primes as,
y=p×q×r, where p, q, r are the prime factors of y ...........(2)

Substituting (2) in (1), we get

x=p×q×r×z .........(3)

Dividing (3) by p we get

xp=z×q×r

Dividing (3) by q we get

xq=z×p×r

Dividing (3) by r we get

xr=z×p×q

Hence, x is divisible by all the prime factors of 'y'.


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