The HCF of 56, 96 and 404 is 4. The largest factor that divides two or more numbers exactly is defined as the Highest Common Factor (HCF). The article HCF in simple language helps students in solving problems based on HCF with ease. Students can make use of this article to cross-check if their method of solving is correct or not. The detailed explanation provided in the article enables students to obtain proficiency in the HCF concept. Let us learn the simple process of how to find the Highest Common Factor of 56, 96 and 404 in a detailed manner.
What is the HCF of 56, 96 and 404
The Highest Common Factor of 56, 96 and 404 is 4 since the number 4 is the largest number that divides the numbers 56, 96 and 404 exactly.
How to Find HCF of 56, 96 and 404?
There are three methods to find the HCF 56, 96 and 404:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 56, 96 and 404 by Prime Factorisation Method
In order to find the HCF using prime factorisation, we express the given numbers as the product of prime factors. Thus, 56, 96 and 404 can be expressed as:
56 = 2 × 2 × 2 × 7
96 = 2 × 2 × 2 × 2 × 2 × 3
404 = 2 × 2 × 101
The common prime factors of 56, 96 and 404 are 2 and 2.
Therefore,
HCF (56, 96, 404) = 2 × 2 = 4
HCF of 56, 96 and 404 by Long Division Method
The following steps are used to find the Highest Common Factor of 56, 96 and 404 using the long division method.
Step 1: Divide the number 404 by the number 56. Here, we get the divisor as 4 when the remainder is zero. Hence, the HCF of 56 and 404 is 4.
Step 2: Now, we perform the long division process on 4 and 96 to calculate the HCF.
Step 3: Here, we get the divisor as 4 when the remainder is zero. Thus, the HCF of 4 and 96 is 4.
The Highest Common Factor of 56, 96 and 404 by the long division method is shown below:
First, find the HCF of 56 and 404.
The HCF of 56 and 404 is 4 and the HCF of 4 and 96 is 4.
Therefore, HCF (56, 96 404) = 4
HCF of 56, 96 and 404 by Listing Common Factors
In this method, we express all the factors of 56, 96 and 404 to find their Highest Common Factor. The largest number among these factors is considered the Highest Common Factor of 56, 96 and 404.
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 404: 1, 2, 4, 101, 202, 404
Therefore, HCF (56, 96, 404) = 4
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Solved Example
Question: Find the highest number that divides 56, 96 and 404 exactly.
Solution: The highest number that divides 56, 96 and 404 exactly is their HCF. Let us list the factors of 56, 96 and 404 to find the Highest Common Factor:
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Factors of 404: 1, 2, 4, 101, 202, 404
Here, 4 is the HCF of 56, 96 and 404.
Therefore, the highest number that divides 56, 96 and 404 is 4.
Frequently Asked Questions on HCF 56, 96 and 404
What is the HCF of 56, 96 and 404?
What are the methods used to find the HCF of 56, 96 and 404?
The methods used to find the HCF of 56, 96 and 404 are:
Prime Factorisation
Long Division method
Listing common factors
The HCF of 56, 96 and 404, and the HCF of 4, 16 and 36 are the same. True or False.
Find the HCF of 56, 96 and 404 using prime factorisation.
In prime factorisation, we express the numbers as the product of prime factors to find the HCF of given numbers.
56 = 2 × 2 × 2 × 7
96 = 2 × 2 × 2 × 2 × 2 × 3
404 = 2 × 2 × 101
The common prime factors of 56, 96 and 404 are 2 and 2.
Therefore, HCF (56, 96, 404) = 2 × 2 = 4
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