If m=dn+r, where m, n are positive integers and d, r are integers, then n is the H.C.F of (m, n) if.

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r = 1

0 < r \leq 1

r = 0

r is a real number.

answer is C.

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Detailed Solution

Concept: let us assume that n is the HCF (m, n). using the fact that if g is HCF of a and b then g divides a and g divides b. we will use the fact that if a is divisible by b, then the remainder obtained on dividing a by b is 0. so find the value of r.
Have,

m = dn + r

Let

HCF (m, n) = n

Knowing that if g is the HCF of a and b, then g divides a and g divides b.
So we have n divides m.
We know that if a is divisible by b then the remainder will be obtained on dividing a by b is 0.
Hence, the correct option is (3).

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