How to find Highest Common Factor (HCF)

 How to find Highest Common Factor (HCF), also named as Greatest Common Factor(GCF), of two or more numbers

METHOD 1:

STEP 1: Write all factors of given numbers.

STEP 2: List common factors.

STEP 3: The biggest common factor is the HIGHEST COMMON FACTOR or HCF of given numbers.

Click here to see the solved example of this method.

METHOD 2:

Let us understand this method by an example.

EXAMPLE: Find Highest Common Factor (HCF) of 158 and 42.

SOLUTION:

STEP 1: Divide the bigger number by the smaller number

Here, 

42 is the divisor

158 is the dividend

3 is the quotient

32 is the remainder

STEP 2: Divide the divisor by remainder. 

In this example, divisor is 42 and remainder is 32.

STEP 3: Keep dividing the previous divisor by remainder until the remainder is zero.

STEP 4: The last divisor is the Highest Common Factor of given numbers.

In this example, 2 is Highest Common Factor (HCF) of 158 and 42.

METHOD 3: This method is mostly used to find Highest Common Factor (HCF) of more than two numbers.

Let us understand this method by an example.

EXAMPLE: Find Highest Common Factor (HCF) of 16, 24, and 40.

SOLUTION:

STEP 1: 

Find a number which divides 16, 24 and 40 completely, leaving no remainder.

It is recommended to start from 2, 3, 4….. one-by-one and check which divides all given numbers, leaving no remainder.

Now, 2 divides 16, 24 and 40, leaving no remainder.

16 ÷ 2 = 8

24 ÷ 2 = 12

40 ÷ 2 = 20

STEP 2: Make table like this

STEP 3: Now again, as did in STEP 1, find a number that divides 8, 12 and 20, leaving no remainder  

Again, 2 divides 8, 12 and 20.

8 ÷ 2 = 4

12 ÷ 2 = 6

20 ÷ 2 = 10

STEP 4: Extend the table like this:

STEP 5: Proceed in the same way until you could not find a number that divides ALL numbers in the right column. 

There is no number that divides 2, 3 and 5 completely, leaving no remainder. 

STEP 6: Multiply all the numbers in the left column.

2×2×2 = 8