The HCF of 126 and 156 is 6. HCF is the greatest integer that can divide 126 and 156 evenly. HCF stands for Highest Common Factor. As the name suggests, for a given set of numbers, there would be common factors, and the highest among the common factors is known as the HCF. In the given set of numbers 126 and 156, the common factors are 1, 2, 3 and 6. Since 6 is the highest among the given factors, HCF would be 6 for 126 and 156. HCF is also termed GCF, which is the Greatest Common Factor. Learn more on HCF.
What is the HCF of 126 and 156?
The Highest Common Factor, also known as the Greatest Common Factor of 126 and 156, is 6.
How to Find HCF of 126 and 156?
There are three methods to find the HCF of 126 and 156:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 126 and 156 by Prime Factorisation Method
In the prime factorisation method, the numbers can be expressed as the product of prime numbers. Here, 126 and 156 can be expressed as:
126 = 2 × 3 × 3 × 7
156 = 2 × 2 × 3 × 13
The common prime factors of 126 and 156 are 2 × 3. Therefore, HCF will be:
HCF (126, 156) = 2 × 3 = 6
HCF of 126 and 156 by Long Division Method
In the long division method, from the given set of numbers, the smaller number is used as the divisor to the larger number. The smaller number is divided by the remainder. This step is repeated till the remainder becomes zero.
Detailed steps are as follows:
- From the given set of numbers, the smallest number becomes the divisor, and the larger number becomes the dividend.
- In the next step, the smaller number becomes the dividend, and the remainder becomes the divisor.
- The above step is followed until the remainder is zero.
- The last divisor would be the HCF.
For 126 and 156, the HCF by long division method is:
Therefore, HCF (126, 156) = 6
HCF of 126 and 156 by Listing Common Factors
By listing common factors of given numbers, we can identify the Highest/Greatest/Biggest Common Factor, which is the HCF. Below is the list of factors for 126 and 156:
Factors of 126:
1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
Factors of 156:
1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156
Therefore, HCF (126, 156) = 6
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the second greatest number that divides 126 and 156.
Solution: The second greatest number that divides 126 and 156 is nothing but the second GCF, which is 3.
2. What is the HCF for 6, 126 and 156?
Solution: The HCF for 6, 126 and 156 is 6, as 6 is the factor for 126 and 156.
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