Tuition Center Singapore Secondary Math Tuition – Highest Common Factor (HCF)

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Tuition Center Singapore Secondary Math Tuition – Highest Common Factor (HCF)

1. The largest common factor among the common factors of two or more numbers is called the highest common factor (HCF) of the given numbers.

Example 1

Factors of 12 are 1, 2, 3, 4, 6, and 12.
Factors of 18 are 1, 2, 3, 6, 9 and 18.

The common factors of 12 and 18 are 1, 2, 3 and 6

Highest common factor of 12 and 18 is 6

2. Another method to find the HCF of two or more numbers is by using prime factorisation which is the more efficient way.

Example 2

Find the highest common factor of 225 and 270.

225 =  3² x 5²
270 = 2 x 3³ x 5

HCF = 3² x 5  = 45

3. We can also repeatly divide the numbers by prime factors to find the HCF

Example 3

Find the highest common factor of 54, 90 and 108.

2) 54, 90, 108
3) 27, 45,  54
3)  9,  15,  18
      3,    5,    6

HCF = 2 x 3 x 3 = 18

The HCF of 54, 90 and 108 is 18.

Application Question

A group of 120 girl guides and 150 boy scouts took part in a camping competition. They were divided exactly into mixed groups. There were the same number of girls and boys in each group.

• What is the largest number of groups that could be formed?
• How many boys and girls are there in each group?

Answer
Largest number of groups = 40
Number of boys in each group = 5
Number of girls in each group = 4

Please contact Angie @ 96790479 or Mr Ong @ 98639633 if you need tuition Lower Secondary Math Tuition