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A number has limited number of factors unlike multiples, so out of these factors what is an HCF?

As the name suggests, HCF is the highest common factor of two or more numbers. In other words, HCF is the biggest number that can divide all the given numbers.

 METHODS TO FIND HCF

There are two methods to find HCF / GCD:-

  1. Prime factorization method
  2. Long division method

Let’s discuss these methods in detail.

  1. Prime factorization method:

Step 1: write prime factors of given numbers.

Step 2:  HCF will be product of least common power of prime number present between / among given numbers.

 Let’s understand it with the help of an example.

Example:  What is the HCF of 18 and 36?

A.18

B.9

C.12

D.36

Answer: Option A

Explanation:

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Step 1 :-

18= 2 x 3 x 3 = 21 x 32
36 = 2 x 2 x 3 x 3 = 22 x 32

Step 2 :-  least power of 2 is 1 and of 3 is 2

Hence 2 x 32 = 18 is required HCF.

You’ll find more questions to practice this method at the end of this article.

  1. HCF by Long Division Method

To find the H.C.F. of the given number using long division method, we will follow the following steps:

  1. We divide the bigger number by smaller one.
  2. Divide smaller number of step 1 with remainder obtained in step 1.
  3. Divide divisor of second step with remainder obtained in step 2.
  4. We will continue this process till we get remainder zero and divisor obtained in end is the required H.C.F.

Example:  Find the HCF of 288 and 600

Solution:

Follow the steps as follows:

Hence required HCF is 24.

Let’s practice these concepts solving the exercise below.

EXERCISE:

Question 1. What is the HCF of 12, 18 and 30?

A. 10

B. 5

C. 6

D. 8

Answer and Explanation

Answer: Option C

Explanation:

12 = 2 x 2 x 3 =22 × 31

18 = 2 x 3 x 3 = 21 x 32

30 =2 x 3 x 5=21 x 31 x 51

Primes involved are 2, 3 and 5 minimum powers involved are 1 ,1 and 0 respectively. Hence

21 x 31 x 50 = 6 is required HCF.

 

Question 2.  Find HCF of  3360, 2240 and 5600.

A. 1000

B. 1120

C. 1630

D. 1210

Answer and Explanation

Answer: Option B

Explanation:

HCF of 3360, 2240 and 5600

 

Question 3 . Find HCF of 304 and 323.

A. 19

B. 50

C. 57

D. 80

Answer and Explanation

Answer: Option A

Explanation:

 

Question 4.  Find HCF of 3015 and 5040 by long division method.

A. 40

B. 50

C. 45

D. 55

Answer and Explanation

Answer: Option C

Explanation:

 

Question 5.  Find HCF of 1651 and 2032 by prime factorization method.

A.197

B.150

C.128

D.127

Answer and Explanation

Answer: Option D

Explanation:

1651 = 13 × 127

2032 = 16 × 12

HCF = 127

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