HIGHEST COMM0N FACTOR (HCF)

COMMON FACTORS

Common factors are those numbers which are factors of all the given numbers.

For example,
12 factors are 1, 2, 3, 4, 6, 12
18 factors are 1, 2, 3, 6, 9, 18
Common factors of 12 and 18 are 1, 2, 3 and 6.

Definition

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

From the above example we found that common factors of 12 and 18 are 1, 2, 3 and 6. What is the highest of these common factors? It is 6.
So we can say that the ,Highest Common Factor (HCF) of 12 and 18 is 6.

Methods of finding HCF

1. Prime Factorisation Method
2. HCF by Continued Division Method

1. Prime Factorisation Method

The HCF of 12, 30 and 36 can also be found by prime factorisation as follows:

2. HCF by Continued Division Method

Divide the larger number by the smaller and then divide the previous divisor by the remainder until the remainder is 0. The last divisor is the HCF of the numbers

1. Find the HCF of 12,16 adn 28.

Thus, HCF of 12, 16 and 28 is 4.

2.Find the HCF of 56 and 64.

DO YOU KNOW?

Can you try this?

1. The length, breadth and height of a room are 12m, 15m and 18m respectively. Determine the longest tape which can measure all the three dimensions of the room exactly?


2. 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.


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