The HCF of 28 and 32 is 4. The Highest Common Factor of 28 and 32 can be denoted as the largest number that divides the numbers 28 and 32 completely without any remainder. The article HCF is the best study guide to clear doubts of students which they come across while solving the problems based on the Highest Common Factor. Here, we will learn the simple steps of how to calculate the Highest Common Factor of 28 and 32 using various methods in a precise manner.
What is the HCF of 28 and 32?
The Highest Common Factor (HCF) of 28 and 32 is 4. There are three common factors of 28 and 32. They are 1, 2 and 4. Hence, the Highest Common Factor (HCF) or the Greatest Common Divisor (GCD) of 28 and 32 is 4.
How to Find HCF of 28 and 32?
Let us look at the methods to find the HCF of 28 and 32:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 28 and 32 by Prime Factorisation Method
In prime factorisation, the numbers can be expressed as the product of prime factors. Here, the numbers 28 and 32 are expressed as:
28 = 2 × 2 × 7
32 = 2 × 2 × 2 × 2 × 2
The common prime factors of 28 and 32 are 2 and 2.
Therefore,
HCF of (28, 32) = 2 × 2 = 4
HCF of 28 and 32 by Long Division Method
Go through the steps given below to find the Highest Common Factor of 28 and 32 using long division.
Step 1: Divide the largest number by the smallest among the given two numbers.
Step 2: Check the remainder; if it is not zero, then make it a new divisor and mention the previous divisor as the new dividend and continue the division process.
Step 3: Repeat this process until we get the remainder equal to zero. The last divisor is considered the HCF of the given two numbers.
The HCF of 28 and 32 by using the long division method is given below:
HCF (28, 32) = 4
HCF of 28 and 32 by Listing Common Factors
In this method, to obtain the HCF, we list out all the factors of 28 and 32. The factors of 28 and 32 are mentioned below:
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 32: 1, 2, 4, 8, 16, 32
Hence, HCF (28, 32) = 4
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Solved Examples
1. What is the highest number that divides both 28 and 32 exactly?
Solution: The highest number that divides both 28 and 32 exactly is their HCF. The factors of 28 and 32 are given below:
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 32: 1, 2, 4, 8, 16, 32
Hence, the HCF of 28 and 32 is 4.
2. What is the LCM if the product of two numbers is 896 and their HCF is 4?
Solution: Given
HCF= 4
Product of numbers = 896
We know that
LCM × HCF = Product of numbers
LCM × 4 = 896
LCM = 224
Therefore, the LCM of 28 and 32 is 224.
Frequently Asked Questions on HCF of 28 and 32
What is the HCF of 28 and 32?
What are the methods used to find the HCF of 28 and 32?
The three methods used to find the HCF of 28 and 32 are as follows:
Prime Factorisation
Long Division Method
Listing Common Factors
Is the HCF of 28 and 32 and the HCF of 4 and 20 the same?
Determine the LCM if the HCF of 28 and 32 is 4.
We know that
HCF × LCM = 28 × 32
Given
HCF = 4
4 × LCM = 28 × 32
LCM = 224
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