The HCF of 32 and 56 is 8. The number 8 is the largest number that divides 32 and 56 exactly, without leaving any remainder. Thus, 8 is the Highest Common Factor (HCF) of 32 and 56. Highest Common Factor is one of the best articles that explains the HCF concept in simple and understandable language in accordance with students’ understanding capacity. Students who want to obtain proficiency in the HCF concept are advised to follow this article as many times as possible. This article explains how to determine the Highest Common Factor of 32 and 56 in a precise manner.
What is the HCF of 32 and 56?
The Highest Common Factor of 32 and 56 is 8. There are four common factors of 32 and 56. They are 1, 2, 4 and 8. Hence, the highest number that divides 32 and 56 completely is 8.
How to Find HCF of 32 and 56?
The three methods to find the HCF of 32 and 56 are:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 32 and 56 by Prime Factorisation Method
In the prime factorisation method, we need to express the numbers as the product of prime factors. Therefore, the given numbers 32 and 56 can be expressed as:
32 = 2 × 2 × 2 × 2 × 2
56 = 2 × 2 × 2 × 7
The common prime factors of 32 and 56 are 2, 2 and 2.
Therefore,
HCF (32, 56) = 2 × 2 × 2 = 8
HCF of 32 and 56 by Long Division Method
In the long division method, the following steps are used to determine the HCF of 32 and 56:
Step 1: Divide the largest number by the smallest number from the given two numbers.
Step 2: Now, check the remainder. If it is not zero, then make it a new divisor and write the previous divisor as the new dividend. Then perform the division.
Step 3: Repeat this process until we get the remainder equal to zero. The last divisor will be considered the HCF of the given two numbers.
The HCF of 32 and 56 by long division method is shown below:
HCF (32, 56) = 8
HCF of 32 and 56 by Listing Common Factors
In this method, we list the factors of the given numbers and then pick the largest of all the common factors. The following are the factors of 32 and 56:
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Hence, HCF (32, 56) = 8
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Solved Examples
1. What is the highest number that divides both 32 and 56 exactly?
Solution: The largest number that divides both 32 and 56 exactly is their HCF. The factors of 32 and 56 are shown below to find the HCF.
Factors of 32: 1, 2, 4, 8, 16, 32
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Here, 8 is the Highest Common Factor of 32 and 56. Hence, the highest number that divides both 32 and 56 is 8.
2. The product of two numbers is 1792. What is the LCM if their HCF is 8?
Solution: Given
HCF = 8
Product of numbers = 1792
We know that
LCM × HCF = Product of numbers
LCM = Product of numbers/HCF
LCM = 1792/8
LCM = 224
Hence, the LCM is 224.
Frequently Asked Questions on HCF of 32 and 56
What is the HCF of 32 and 56?
How to find the HCF of 32 and 56 by prime factorisation?
In prime factorisation method, we express the given numbers as the product of prime factors. Therefore, the numbers 32 and 56 can be represented as:
32 = 2 × 2 × 2 × 2 × 2
56 = 2 × 2 × 2 × 7
The common prime factors of 32 and 56 are 2, 2 and 2
Therefore, HCF (32, 56) = 2 × 2 × 2 = 8
What are the common factors of 32 and 56?
Name the methods used to find the HCF of 32 and 56.
The methods used to find the HCF of 32 and 56 are as follows:
Prime Factorisation
Long Division method
Listing common factors
If the HCF of 32 and 56 is 8, what is their LCM?
We know that
HCF × LCM = 32 × 56
Given
HCF = 8
8 × LCM = 32 × 56
LCM = 224
Hence, the LCM is 224.
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