HCF of 72 and 126

The HCF of 72 and 126 is 18. Listing common factors, prime factorisation, and long division are the three most frequent methods for calculating the HCF of 72 and 126. The greatest number that can divide 72 and 126 perfectly without leaving a remainder is the HCF of these numbers. Factors of 72 and 126 are (1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and (1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126), respectively.

Also read: Highest common factor

What is the HCF of 72 and 126?

The answer to this question is 18. This article shows how to find the HCF of 72 and 126 using various methods for your reference. The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers.

How to Find HCF of 72 and 126?

There are three methods to find the HCF of 72 and 126:

  • Prime Factorisation
  • Long Division method
  • Listing common factors

HCF of 72 and 126 by Prime Factorisation Method

The prime factorisation of 72 and 126 is given by:

Prime factorisation of 72 = (2 × 2 × 2 × 3 × 3)

Prime factorisation of 126 = (2 × 3 × 3 × 7)

The HCF of 72 and 126 is 2 × 3 × 3 = 18.

Hence, HCF (72, 126) = 18

HCF of 72 and 126 by Long Division Method

The divisor that we receive when the remainder becomes 0 after executing a long division repeatedly is the HCF of 72 and 126.

HCF of 72 and 126 1 HCF of 72 and 126 2 HCF of 72 and 126 3

No further division can be done. 

Hence, HCF (72, 126) = 18

HCF of 72 and 126 by Listing Common Factors

To calculate the HCF of 72 and 126 by listing out the common factors, list the factors as shown below:

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126

There are 6 common factors of 72 and 126, and they are 1, 2, 3, 6, 9, and 18. Therefore, the highest common factor of 72 and 126 is 18.

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Video Lesson on Properties of HCF and LCM

Solved Example

Find the HCF of 72 and 126, if their LCM is 504.

Solution:

We know that LCM × HCF = 72 × 126

⇒ HCF(72, 126) = (72 × 126)/504 = 18

 HCF(72, 126) = 9072/504 = 18

Therefore, the highest common factor of 72 and 126 is 18.

Frequently Asked Questions on HCF of 72 and 126

Q1

What is the HCF of 72 and 126?

The HCF of 72 and 126 is 18. To calculate the Highest common factor (HCF) of 72 and 126, we need to factor each number and choose the highest factor that exactly divides both 72 and 126, i.e. 18.
Q2

How to find the HCF of 72 and 126 by prime factorisation?

To find the HCF of 72 and 126, we will find the prime factorisation of the given numbers, i.e. 72 = 2 × 2 × 2 × 3 × 3; 126 = 2 × 3 × 3 × 7. ⇒ Since 2, 3 and 3 are common factors in the prime factorisation of 72 and 126, HCF(72, 126) = 2 × 3 × 3 = 18
Q3

What are the methods to find HCF of 72 and 126?

There are three commonly used methods to find the HCF of 72 and 126. They are: Long Division Listing Common Factors Prime Factorisation
Q4

What is the relation between LCM and HCF of 72, 126?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 72 and 126, i.e. HCF × LCM = 72 × 126 = 9072.
Q5

How to find the HCF of 72 and 126 by long division method?

To find the HCF of 72, 126 using the long division method, 126 is divided by 72. The corresponding divisor (18) when remainder equals 0 is taken as HCF.

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