The HCF of 56 and 84 is 28. HCF stands for Highest Common Factor, and as the name suggests, the number that is highest among the common factors is known as HCF. It can also be referred to as GCD (Greatest Common Divisor) or GCF (Greatest Common Factor). For the given set of numbers 56 and 84, 28 is the HCF/GCD/GCF. Even though there are other common factors, like 1, 2, 4, 7, 14 and 28, 28 is greater than the other common factors. You can refer to the HCF and LCM to understand the difference between the two.
What is the HCF of 56 and 84?
The Highest Common Factor, also known as the Greatest Common Factor of 56 and 84, is 28.
How to Find HCF of 56 and 84?
There are three methods to find the HCF of 56 and 84:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 56 and 84 by Prime Factorisation Method
In the prime factorisation method, the numbers can be expressed as the product of prime numbers. Here, 56 and 84 can be expressed as:
56 = 2 × 2 × 2 × 7
84 = 2 × 2 × 3 × 7
The common prime factors are 2, 2 and 7. Therefore, HCF will be:
HCF (56, 84) = 2 × 2 × 7 = 28
HCF of 56 and 84 by Long Division Method
In the long division method, the following steps are followed.
- 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 56 and 84, the HCF by long division method is:
Therefore, HCF (56, 84) = 28
HCF of 56 and 84 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 56 and 84:
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Therefore, HCF (56, 84) = 28
Related Articles
Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the second greatest number that divides 56 and 84 evenly.
Solution: The common factors of 56 and 84 are 1, 2, 4, 7, 14 and 28. The second greatest number that divides 56 and 84 evenly is 14.
2. What is the GCF of 6 and 5?
Solution: The GCF of 6 and 5 is 1.
Comments