In this article, you will learn how to find Highest Common Factor by using the Prime Factorization Method. The highest number among all the common factors of the given numbers is known as the Highest Common Factor(HCF) of a number. It is also referred to as a (Greatest Common Factor).

For better understanding and more practice purposes, we will provide various questions with a quick explanation here. We have covered different models of questions on HCF using the prime factorization method, procedure on how to find hcf by prime factorization. Assess your strengths and weaknesses on the concept by finding the Highest Common Factor of Numbers as a part of your preparation.

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### Highest Common Factor – Definition

HCF is defined as the highest common factor of all the given numbers. The number that can divide exactly two or more given numbers without any remainder. It is also known as the Greater Common Factor (GCF) or Greatest Common Divisor (GCD). The simplest way to find the HCF of two given numbers is to create a Factor Tree.

### Prime Factorization – Definition

Prime Factorization is defined as a technique of finding the prime factors of two or more numbers, such that the initial number is divisible by these factors. We know, the composite number has more than two factors. Therefore, this method is just applicable to composite numbers and not for prime numbers.

### How to Find HCF of Numbers using Prime Factorization?

For calculating Highest Common Factor using Prime Factorization Method, we need to factorize the numbers into Prime Factors. The following are the steps to find the HCF of a given number using the Prime Factorization Method,

Step 1: Initially, check whether the given number is divisible by 2 or not.

Step 2: Now, divide the number until you cannot divide any further.

Step 3: Finally, write the numbers as the product of the prime numbers. The product of those common factors is that the Highest Common Factor of the given numbers.

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### HCF by Prime Factorization Method Examples

**Example 1: **

Find the H.C.F of three numbers 28, 36, 44 by Prime Factorization Method?

**Solution:
**Given the values are 28, 36, 44

Now, first, we’ve to write down the factors of the given three numbers.

The factors of 28 are 1, 2, 4, 7, 14, and 28.

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Factors of 44 are 1, 2, 4, 11, and 44.

Now, we’ve to write down the common factors of all the three given numbers.

The Common Factors of 28, 36, 44 = 1, 2, 4.

So, the HCF of three given numbers is 4.

**Example 2:**

Find the Prime Factorization Division Method of

(i)50

(ii)80

**Solution:**

(i) Given the number,

First, divide the number 50 using the smallest prime number that is 2.

50÷2 =25

Next, divide the quotient with the next smallest prime number.

25÷ 5= 5

Now, again divide that quotient with the prime number.

5÷5 =1

Hence, 5 may be a prime number the division process ends here.

The Prime Factors of 50 are 5.

Hence, the HCF of 50 using the division method is 5.

(ii) The value is 80,

First, divide the number 80 using the smallest prime number that is 2.

80÷2 =40

Next, divide the quotient with the smallest prime number.

40÷ 2= 20

Now, again divide that quotient with the next smallest prime number.

20÷2 =10

Again, divide that quotient with the prime number of two.

10÷2 =5

Divide 5 with another least prime number.

5÷5 =1

Hence, 5 could also be a prime number the division process ends here.

The Prime Factors of 80 are 2 x 2 x 2 x 2 x 5.

Hence, the Highest Common Factor of 80 is 5.

**Example 3: **

Using the Prime Factorization find the HCF value of 61 and 63

**Solution:**

Given the values 61 and 63.

Now, write the factors

The Factors of 61 are 1, and 61.

The factors of 63 are 1, 3, 7, 9, and 63

Therefore the common factors of 61 and 63 are 1

Therefore, 1 is the Highest Common Factor of given numbers.

**Example 4: **

What is the HCF of 84, 62?

**Solution: **

As given within the question, the values are 84 and 62.

Now, write the factors using prime factors.

The factors are 2 x 2 x 3 x 7.

Now, finding 62 factors,

The factors are 2 x 31.

The Highest Factor of the given number is 2.

**Example 5:**

What is the HCF of 36 and 72 using the Prime Factorization Method?

**Solution:**

Given the values 36 and 72.

Using Prime Factorization Method, we need to find the HCF value.

First, write the prime factors.

The Prime Factorization of 36 is 2 x 3 x 6

The Prime Factorization of 72 is 2 x 2 x 3 x 6

So, the common factors of 36 and 72 are 2 x 3

Thus, the HCF of the two given numbers is 2 x 3 is 6.