Highest common factor (HCF)

The highest (greatest) common factor is the biggest common factor of two or more numbers. To calculate it, we decompose all numbers in prime factors and multiply only the common factors to the minimum index. If there isn't a common factor, the HCF is 1. In this case, we call those numbers coprimes.

Example: Calculate the highest common factor of 20 and 30

20 = 2² · 5     

30 = 2 · 3 · 5

 

hcf (20, 30) = 2 · 5 = 10

 

 

Exercises:

1.-Calculate the HCF of:

a) 8, 12 and 16

b) 12, 15 and 20

c) 30, 45 and 75

 

2.- Julia wants to build a square as small as possible by joining rectangular pieces of 12x18 cm. How much does the square side measure? How many pieces does she use?

 

 

 

Solutions: 1.- a) 4; b) 1 (they are coprimes); c) 15; 2.- 6 cm; 6 pieces