Hcf (hsp)

H.C.F BY : Mrs. Santosh Puri

DEFINITION H.C.F. is the highest common factor of two or more than two number’s e.g. 12 are 1,2,3,4,6,12 18 are 1,2,3,6,9,18 The highest common factor among 12,18 is 6

Different Ways of finding H.C.F. Factorization Prime factorization Continuous division

FACTORIZATION In this method we write down the possible factors of each number and then observe the H.C.F out of them.

e.g. H.C.F of 8,12,16 The factor of each are as  8=1,2,4  12=1,2,3,4,6,12  16=1,2,4,8,16 The common factor are 1,2,4 The highest common factor is 4,therefore 4 is the H.C.F of 8,12,16

PRIME FACTORIZATION In this method we write the prime factors of each number,then we find out the common prime factors.In the last we multiply the common prime factors.

E.g. To find the H.C.F of 24,36 First we find out the prime factors of 24,36 24=2*2*2*3 36=2*2*3*3 The common prime factors are2,2,3 H.C.F=2*2*3=12 In case there is no common factor then,H.C.F=1

CONTINUOUS DIVISION METHOD In this method,we divide the greater number by smaller number,if the remainder is 0,then smaller number will be the H.C.F.In case the remainder is not 0,then we divide the smaller number by remainder.Now again if the remainder is 0,then the divisor will be the H.C.F.But if remainder is not 0,then we divide last divisor by this remainder.Continue this until remainder is 0,the last divisor will be H.C.F.

e.g H.C.F of 32,56 32)56(1 32 24)32(1 24 8)24(3 24 0 H.C.F of 32,56 is 8