Greatest Common Divisor definition (dave hook)

The greatest common divisor of 2 or more without zero integers, is the biggest +ve integer that is divide the all numbers lacking a remainder The another name of the greatest common divisor is the greatest factor(gcf), greatest common denominator, highest common divisor. For example greatest common divisor of 8 and 12 is 4.Now we see about the Greatest common divisor definition.

Greatest common divisor definition Examples:

Greatest common divisor definition Example 1:

Find the greatest common divisor of given numbers 48, 180

Solution:

48 is written by 48 = 2 x 2 x 2 x 2 x 3

180 is written by 180 = 2 ? 2 ? 3 ? 3 ? 5.

Therefore the greatest common divisor = 2 x 2 x 3 = 12

Greatest common divisor definition Example 2:

Find the greatest common divisor of given numbers 21, 15

Solution:

21 is written by 21 = 3 x 7

15 is written by 15 = 3 x 5

Therefore the greatest common divisor = 3

Greatest common divisor definition Example 3:

Find the greatest common divisor of given numbers 15, 21, 18

Solution:

15 is written by 15 = 3 x 5

21 is written by 21 = 3 x 7

18 is written by 18 = 3 x 3 x 2

Therefore the greatest common divisor = 3

Greatest common divisor definition Example 4:

Find the greatest common divisor of given numbers 15, 21

Solution:

15 is written by 15 = 3 x 5

21 is written by 21 = 3 x 7

Therefore the greatest common divisor = 3

Greatest common divisor definition More Examples:

Greatest common divisor definition Example 1:

Find the greatest common divisor of given numbers 25, 65

Solution:

25 is written by 25 = 5 x 5

65 is written by 65 = 5 x 13

Therefore the greatest common divisor = 5

Greatest common divisor definition Example 2:

Find the greatest common divisor of given numbers 8, 64, 128

Solution:

8 is written by 8 = 2 x 2 x 2

64 is written by 64 = 2 x 2 x 2 x 2 x 2 x 2

128 is written by 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2

Therefore the greatest common divisor = 2 x 2 x 2 = 8

Greatest common divisor definition Example 3:

Find the greatest common divisor of given numbers 8, 18

Solution:

8 is written by 8 = 2 x 2 x 2

18 is written by 18 = 2 ? 3 ? 3.

Therefore the greatest common divisor = 2

Preparation for greatest common factor - example problems.

here we are going to prepare some example problems for gcf

Preparation example: 1

Find the greatest common denominator for 18, 16 using prime factorization method.

Solution:

First we have to find the prime factor for each number

Prime factor for 18 = 2, 3, 3

Prime factor for 16 = 2, 2, 2, 2

Here the common terms for both = 2

Therefore the gcf of given number is = 2

Preparation example: 2

Find the greatest common factor for 55,121

Solution:

First we have to find the prime factors for each

Prime factor for 55 = 5, 11

Prime factor for 121 = 11,11

Here the common term = 11

Therefore the gcf of 55, 121 = 11

Preparation for greatest common factor - example: 3

Preparation example: 3

Find the greatest common factor for 48, 124, and 76

Solution:

First we have to find the prime factor for each one

Prime factor for 48 = 2, 2, 2, 2, 3

Prime factor for 124 = 2,2, 31

Prime factor for 76 = 2,2,19

Here the common factor is 2, 2

Therefore the gcf of given number is 2 * 2 = 4

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