The HCF of 403, 434 and 465 is 31. The Highest Common Factor (HCF) of two or more numbers is the largest number that is a factor of all the numbers. It is also called the Greatest Common Divisor (GCD). HCF is one of the best articles that provide basic information on how to find the Highest Common Factor of given numbers. Students who refer to this article while solving the problems will definitely gain a stronghold on the HCF concept. In this article, let us learn the technique of determining the Highest Common Factor of 403, 434 and 465 accurately.
What is the HCF of 403, 434 and 465?
The Highest Common Factor of 403, 434 and 465 is 31 since the number 31 is the largest number that divides the numbers 403, 434 and 465 exactly.
How to Find HCF of 403, 434 and 465?
There are three methods to find the HCF 403, 434 and 465:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 403, 434 and 465 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, 403, 434 and 465 can be expressed as;
403 = 13 × 31
434 = 2 × 7 × 31
465 = 3 × 5 × 31
The Common prime factor of 403, 434 and 465 is 31.
Therefore,
HCF (403, 434, 465) = 31
HCF of 403, 434 and 465 by Long Division Method
The below steps are used to find the Highest Common Factor of 403, 434 and 465 using the long division method.
Step 1: Divide the number 434 by the number 403. Here, we get the divisor as 31 when the remainder is zero. Hence, the HCF of 434 and 403 is 31.
Step 2: Now, we perform the long division process on 31 and 465 to calculate the HCF.
Step 3: Here, we get the divisor as 31 when the remainder is zero. Thus, the HCF of 31 and 465 is 31.
The Highest Common Factor of 403, 434 and 465 by the long division method is shown below;
HCF of 403 and 434 is 31 and HCF of 31 and 465 is 31
Therefore, HCF (403, 434, 465) = 31.
HCF of 403, 434 and 465 by Listing the Factors
In this method, we express all the factors of 403, 434 and 465 to find their Highest Common Factor. The largest number among these factors is considered the Highest Common Factor of 403, 434 and 465.
Factors of 403: 1, 13, 31, 403
Factors of 434: 1, 2, 7, 14, 31, 62, 217, 434
Factors of 465: 1, 3, 5, 15, 31, 93, 155, 465
Therefore, HCF (403, 434, 465) = 31
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Solved Example
Question: Calculate the highest number that divides 403, 434 and 465 exactly.
Solution: The highest number that divides 403, 434 and 465 exactly is their HCF. Let us list the factors of 403, 434 and 465 to find the highest number:
Factors of 403: 1, 13, 31, 403
Factors of 434: 1, 2, 7, 14, 31, 62, 217, 434
Factors of 465: 1, 3, 5, 15, 31, 93, 155, 465
Here, 31 is the HCF of 403, 434 and 465
Therefore, the highest number that divides 403, 434 and 465 is 31.
Frequently Asked Questions on HCF 403, 434 and 465
What is the HCF of 403, 434 and 465?
What are the methods used to find the HCF of 403, 434 and 465?
The methods used to find the HCF of 403, 434 and 465 are given below:
Prime Factorisation
Long Division method
Listing common factors
The HCF of 403, 434 and 465 and the HCF of 31, 62 and 124 are the same. True or False.
Determine the HCF of 403, 434 and 465 using prime factorisation.
In prime factorisation, we express the numbers as the product of prime factors to find the HCF of given numbers.
403 = 13 × 31
434 = 2 × 7 × 31
465 = 3 × 5 × 31
Common prime factor of 403, 434 and 465 is 31
Therefore, the HCF of 403, 434 and 465 is 31
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