# Highest Common Factor (HCF)

You can find the common factors of any two numbers. For example, the common factors of 12 and 16 are 1, 2 and 4. The highest of these common factors is 4.

The Highest Common Factor (HCF) of two or more given numbers is the highest (or greatest) of their common factors. It is also known as Greatest Common Divisor (GCD).

For example, the HCF of 20, 28 and 36 can also be found by prime factorisation of these numbers.

20 = 2 × 2 × 5

28 = 2 × 2 × 7

36 = 2 × 2 × 3 × 3

The common factor of 20, 28 and 36 is 2 (occurring twice). Thus, HCF of 20, 28 and 36 is 2 × 2 = 4.

Example 1: Two tankers contain 850 litres and 680 litres of kerosene oil respectively. Find the maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times.

The required container has to measure both the tankers in a way that the count is an exact number of times. So its capacity must be an exact divisor of the capacities of both the tankers. Moreover, this capacity should be maximum. Thus, the maximum capacity of such a container will be the HCF of 850 and 680.

Hence,

850 = 2 × 5 × 5 × 17

680 = 2 × 2 × 2 × 5 × 17

The common factors of 850 and 680 are 2, 5 and 17.

Thus, the HCF of 850 and 680 is 2 × 5 × 17 = 170.

Therefore, maximum capacity of the required container is 170 litres. It will fill the first container in 5 and the second in 4 refills.