The HCF of 64 and 72 is 8. The Highest Common Factor (HCF) can be represented as the largest number among all the common factors of given numbers. Learning the HCF concept is vital among students as it is one of the most important concepts in Mathematics. For more conceptual knowledge, students can follow the article HCF formulated by highly experienced teachers after conducting vast research on the Highest Common Factor. In this article, we will learn the simple methods of calculating the Highest Common Factor of 64 and 72.
What is the HCF of 64 and 72?
The answer to this question is 8. The factors of 64 are 1, 2, 4, 8, 16, 32, 64, and the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Therefore, the largest number that divides both 64 and 72 is 8. 6
How to Find HCF of 64 and 72?
There are three methods to find the HCF of 64 and 72:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 64 and 72 by Prime Factorisation Method
In prime factorisation, we write the numbers as the product of prime factors. To obtain the Highest Common Factor, multiply all the common prime factors with the lowest degree (power).
64 = 2 × 2 × 2 × 2 × 2 × 2
72 = 2 × 2 × 2 × 3 × 3
The common prime factors of 64 and 72 are 2, 2 and 2.
Therefore,
HCF of (64, 72) = 2 × 2 × 2 = 8
HCF of 64 and 72 by Long Division Method
The below steps are used to find the Highest Common Factor of 64 and 72:
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: Continue this process until we get the remainder as zero. The last divisor will be the HCF of the given two numbers.
The HCF of 64 and 72 by the long division method is as follows:
HCF (64, 72) = 8
HCF of 64 and 72 by Listing Common Factors
In this method, we list all the factors of given numbers to find the Highest Common Factor. The factors of 64 and 72 are given below:
Factors of 64: 1, 2, 4, 8, 16, 32, 64
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Hence, HCF (64, 72) = 8
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Solved Examples
1. What is the HCF of 64 and 72 if their LCM is 576?
Solution: We know that
LCM × HCF = 64 × 72
576 × HCF = 4608
HCF = 8
2. What is the highest number that divides 64 and 72 exactly?
Solution: The highest number that divides 64 and 72 is their HCF. Let us have a look at the factors of 64 and 72 given below:
Factors of 64: 1, 2, 4, 8, 16, 32, 64
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Here, the HCF of 64 and 72 is 8.
Hence, the highest number that divides 64 and 72 exactly is 8.
Frequently Asked Questions on HCF of 64 and 72
What is the HCF of 64 and 72?
Name the methods used to find the HCF of 64 and 72.
The methods used to find the HCF of 64 and 72 are as follows:
Prime Factorisation
Long Division Method
Listing Common Factors
Find the HCF of 64 and 72 using the prime factorisation method.
Here, we represent the given numbers as the product of prime factors
64 = 2 × 2 × 2 × 2 × 2 × 2
72 = 2 × 2 × 2 × 3 × 3
The common prime factors of 64 and 72 are 2, 2 and 2.
Therefore, HCF of (64, 72) = 2 × 2 × 2 = 8
What is the LCM if the HCF of 64 and 72 is 8?
We know that
HCF × LCM = 64 × 72
Given
HCF = 8
8 × LCM = 64 × 72
LCM = 576
Hence, the LCM is 576
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