The HCF of 657 and 963 is 9. HCF of 657 and 963 is the greatest integer that can divide both numbers evenly. HCF stands for Highest Common Factor. For a given set of numbers, there would be common factors, and as the name suggests, the highest among them is known as the HCF. In the given set of numbers 657 and 963, the common factors are 1, 3 and 9. Since 9 is the highest among the common factors, HCF would be 9 for 657 and 963. HCF is also termed GCF, which is the Greatest Common Factor. Learn more on GCF.
What is the HCF of 657 and 963?
The Highest Common Factor, also known as the Greatest Common Factor, of 657 and 963 is 9.
How to Find HCF of 657 and 963?
There are three methods to find the HCF of 657 and 963:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 657 and 963 by Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 657 and 963 can be expressed as:
657 = 3 × 3 × 73
963 = 3 × 3 × 107
Common prime factors are 3 and 3. Therefore, HCF will be,
HCF (657, 963) = 3 × 3 = 9.
HCF of 657 and 963 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 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 657 and 963, the HCF by Long Division method is:
Therefore, HCF (657, 963) = 9
HCF of 657 and 963 by Listing Common Factors
By listing all the factors of given numbers, we can identify the Highest/Greatest/Biggest common factor, which is the HCF. Below is the list of factors for 657 and 963:
Factors of 657: 1, 3, 9, 73, 219, 657
Factors of 963: 1, 3, 9, 107, 321, 963
Therefore, HCF (657, 963) = 9
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the second greatest number that divides 657 and 963.
Solution: The second greatest number that divides 657 and 963 is nothing but the second GCF, which is 3.
2. What is the HCF for 9, 657 and 963?
Solution: The HCF for 9, 657 and 963 is 9, as 9 is the factor for 657 and 963.
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