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.
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.
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