## GREATEST COMMON DIVISOR

GREATEST COMMON DIVISOR :Specific Objectives

By the end of the topic the learner should be able to:

- Find the GCD/HCF of a set of numbers.
- Apply GCD to real life situations.

Content

- GCD of a set of numbers
- Application of GCD/HCF to real life situations

**Introduction**

A Greatest Common Divisor is the largest number that is a factor of two or more numbers.

When looking for the Greatest Common Factor, you are only looking for the COMMON factors contained in both numbers. To find the G.C.D of two or more numbers, you first list the factors of the given numbers, identify common factors and state the greatest among them.

The G.C.D can also be obtained by first expressing each number as a product of its prime factors. The factors which are common are determined and their product obtained.

Example

Find the Greatest Common Factor/GCD for 36 and 54 is 18.

Solution

The prime factorization for 36 is 2 x 2 x 3 x 3.

The prime factorization for 54 is 2 x 3 x 3 x 3.

They both have in common the factors 2, 3, 3 and their product is 18.

That is why the greatest common factor for 36 and 54 is 18.

Example

Find the G.C.D of 72, 96, and 300

**Solution**

72 | 96 | 300 | |

2 | 36 | 48 | 150 |

2 | 18 | 24 | 75 |

3 | 6 | 8 | 25 |

Past KCSE Questions on the topic

- Find the greatest common divisor of the term. 144x
^{3}y^{2}and 81xy^{4} - Hence factorize completely this expression 144x
^{3}y^{2}-81xy^{4}(2 marks) - The GCD of two numbers is 7and their LCM is 140. if one of the numbers is 20, find the other number
- The LCM of three numbers is 7920 and their GCD is 12. Two of the numbers are 48 and 264. Using factor notation find the third number if one of its factors is 9

ALL MATHEMATICS NOTES FORM 1-4 WITH TOPICAL QUESTIONS & ANSWERS

PRIMARY NOTES, SCHEMES OF WORK AND EXAMINATIONS