GREATEST COMMON DIVISOR (G.C.D)

BACKGROUND KNOWLEDGE

Find our common factors (Common divisors)

Factor - If a number can be divided by another number

without a remainder, the second number is a factor of the first.

Worked out examples

Find the divisors/ factors of the following set of numbers

1. 20 ,32 2. 36 , 48 ,60

SOLUTION

1. 20 - its divisors are {1, 2, 4, 5, 10, 20}

32 - It's divisors are { 1, 2, 4, 8, 16, 32}

The common divisors are {1, 2, 4}

2. 

36 - It's divisors are { 1, 2, 3, 4, 6, 12, 18, 36}

48 - It's divisors are { 1, 2, 3, 4, 6, 8, 12, 16, 24, 48}

60 - It's divisors are { 1, 32, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}

The common divisors are { 1, 2, 3, 4, 6, 12}

1. Expressing numbers as products of prime factors:

24 = 2 x 2 x 2 x 2 = 2³x 3

8 = 2 x 2 x 2 = 2³

36 = 2 x 2 x 3 x 3 = 2² x 3²

25 = 5 x 5 = 5²

2. Finding G.C.D of a set numbers

a). Find the G.C.D of 36, 48, 60

36 = 2 x 2 x 3 x 3 = 2²x 3²

48 = 2 x 2x 2 x 2 x3 = 2⁴x 3

60 = 2 x 2 x 3 x 5 = 2²x 3 x 5

2²and 3 are common factors

G.C.D = 2²x 3

= 12

3. Divisibility test for prime numbers, that is 2, 3, 5, 11

A number is divisible by:

2 - If the last digits is zero or even e.g 30,102, 6, 76

3 - If the sum of the digits are divisible by 3 ,

for example 1 2 3 -{1+ 2 + 3 = 6}

34 5 - { 3 + 4 + 5 = 12}

2 0 4 -{ 2 + 0 + 5 = 6}

5 - If the last digit is 0 or 5 e.g. 50, 65, 70

11 - If the last sum of the alternate digit are equal

or their difference is a multiple of 11,

e.g 1 8 7 - ( 1 +7) - 8 = 0

8 1 9 3 9 - {8 + 9 + 9} -{1 +3} = 22