The HCF of 404 and 96 is 4. The Highest Common Factor (HCF) is the largest possible integer that divides the given numbers without leaving a remainder. The article HCF of Two Numbers provides in-depth information on HCF to enable students to understand the concept effectively. There are three methods to find the HCF of given numbers. They are prime factorisation, long division method and listing common factors. 1, 2, and 4 are the three common factors of 404 and 96. Let us grasp the simple tricks of how to determine the Highest Common Factor of 404 and 96 with a complete explanation in this article.
What is the HCF of 404 and 96?
The Highest Common Factor (HCF) or the Greatest Common Divisor (GCD) of 404 and 96 is 4. The factors of 404 and 96 are 1, 2, 4, 101, 202, 404 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, respectively.
How to Find HCF of 404 and 96?
There are three methods to find the HCF of 404 and 96:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 404 and 96 by Prime Factorisation Method
In the prime factorisation method, we express the given numbers as the product of prime factors. Therefore, 404 and 96 can be expressed as;
404 = 2 × 2 × 101
96 = 2 × 2 × 2 × 2 × 2 × 3
Common prime factors of 404 and 96 are 2 and 2.
Hence,
HCF (404, 96) = 2 × 2 = 4
HCF of 404 and 96 by Long Division Method
We use the following steps to find the Highest Common Factor of 404 and 96 in the division method.
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 the HCF of the given two numbers.
The HCF of 404 and 96 by the long division method is as follows:
Hence, HCF (404, 96) = 4
HCF of 404 and 96 by Listing the Factors
In this method, by listing all the factors of given numbers, we can find the Highest Common Factor. The factors of 404 and 96 are as follows:
Factors of 404:1, 2, 4, 101, 202, 404
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Hence, HCF (404, 96) = 4
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. What is the highest number that divides both 404 and 96 exactly?
Solution: The Highest Common Factor of 404 and 96 is 4. Hence, the highest number that divides both 404 and 96 exactly is 4.
2. What is the HCF of 404 and 96 if their LCM is 9696?
Solution:
Given
LCM = 9696
We know that
LCM × HCF = 404 × 96
9696 × HCF = 404 × 96
HCF (404, 96) = (404 × 96) / 9696
HCF (404, 96) = 38784 / 9696 = 4
Therefore the HCF of 404 and 96 is 4.
Frequently Asked Questions on HCF of 404 and 96
What is the HCF of 404 and 96?
Is the HCF of 404 and 96 the same as the HCF of 4 and 8?
What are the methods used to find the HCF of 404 and 96?
The methods used to find the HCF of 404 and 96 are as follows:
Prime Factorisation
Long Division method
Listing common factors
How to find the HCF of 404 and 96 by prime factorisation?
To find the HCF of 404 and 96 by prime factorisation, we need to express the numbers as the product of prime factors
404 = 2 × 2 × 101
96 = 2 × 2 × 2 × 2 × 2 × 3
Common prime factors of 404 and 96 are 2 and 2
HCF (404, 96) = 2 × 2 = 4
Therefore, HCF of 404 and 96 is 4
Write the relation between LCM and HCF of 404 and 96.
The equation used to denote the relation between LCM and HCF of 404 and 96 is given below:
HCF × LCM = 404 × 96
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