The HCF of 306 and 657 is 9. HCF of 306 and 657 is the greatest integer that can divide both numbers 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 306 and 657, the common factors are 1, 3 and 9. Since 9 is the highest among the given factors, HCF will be 9 for 306 and 657. HCF is also termed GCF, which is the Greatest Common Factor. Learn more on GCF.
What is the HCF of 306 and 657?
The Highest Common Factor, also known as the Greatest Common Factor, of 306 and 657 is 9.
How to Find HCF of 306 and 657?
There are three methods to find the HCF of 306 and 657:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 306 and 657 by Prime Factorisation Method
In the Prime Factorisation, the numbers can be expressed as the product of prime numbers. Here, 306 and 657 can be expressed as:
306 = 2 × 3 × 3 × 17
657 = 3 × 3 × 73
Common Prime Factors are 3 and 3. Therefore HCF will be,
HCF (306, 657) = 3 × 3 = 9.
HCF of 306 and 657 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. Next, the lesser number or the other number is divided by the remainder of the previous division. This step is repeated until 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.
Following the above steps for 306 and 657, the HCF would be;
Hence, HCF (306, 657) = 9
HCF of 306 and 657 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 306 and 657:
Factors of 306:
1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306
Factors of 657:
1, 3, 9, 73, 219, 657.
Hence, HCF (306, 657) = 9
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the second greatest number that divides 306 and 657.
The second greatest number that divides 306 and 657 is nothing but the second GCF, which is 3.
2. What is the HCF for 9, 306 and 657?
The HCF for 9, 306 and 657 is 9, as 9 is the factor for 306 and 657.
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