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