GREATEST COMMON DIVISOR (G.C.D)

Introduction

Given the following set of numbers, find the G.C.D/H.C.F by listing factors:

Worked out examples

a). 36, 54, 72

36= 1,2,3,4,6,9,12,18,36

54= 1,2,3, ,6,9, 18,27,54

72= 1,2,3,4,6,9,12,18,24,36,72

The common factors are: { 1, 2, 3, 6, 9, 18}

The greatest common divisor/factor is 18

Therefore the G.C.D/HCF of 36, 54 and 72 is 18

G.C.D/H.C.F can also be determined by using prime factorization

To find G.C.D/H.C.F of a set of numbers:

i). Express each number as a product of prime factor

ii). Find the common prime factors

iii). multiply the common prime factors together to give GCD/H.C.F

Find the G.C.D/H.C.F for the following set:

{ 60, 90, 135 }

60= 2x 2 x 3x 5

90= 2x3x 3x5

135= 3x3x 3 x5

Common prime factors are 3 and 5

G.C.D/H.C.F = 3 x 5 = 15