Page 18 - 新思维数学学生用书7 样章

1.4 Highest common factors

1.4 Highest common factors

In this section you will … Key words

• find out about highest common factors. common factor

factor
The factors of 18 are 1, 2, 3, 6, 9 and 18.
The factors of 27 are 1, 3, 9 and 27. highest common

The common factors of 18 and 27 are 1, 3 and 9. factor
The highest common factor (HCF) of 18 and 27 is 9.
Tip

18 = 1 × 18 or 2 × 9 or 3 × 6.
9 is the largest factor of both
18 and 27.

Worked example 1.7

Find the highest common factor of 28 and 42.

Answer
Find pairs of whole numbers that have a
product of 28.

28 = 1 × 28 28 = 2 × 14 28 = 4 × 7
The factors of 28 are 1, 2, 4, 7, 14 and 28.
Find pairs of whole numbers that have a
product of 42.

42 = 1 × 42 = 2 × 21 = 3 × 14 = 6 × 7
The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
The common factors are 1, 2, 7 and 14. The common factors are in both of the lists of
The highest common factor of 28 and 42 is 14. factors.

You can use a highest common factor to simplify a fraction as much as possible.

17