The HCF of 455 and 42 is 7. HCF stands for Highest Common Factor, and as the name suggests, the number that is highest among the common factors is known as HCF. It can also be referred to as GCD, Greatest Common Divisor or GCF, Greatest Common Factor. For the given set of numbers 455 and 42, 7 is the HCF/GCD/GCF, as 1 and 7 are the only two common factors, and 7 is greater than 1. You can refer to the Highest Common Factor for more details.
What is the HCF of 455 and 42?
The Highest Common Factor, also known as the Greatest Common Factor, of 455 and 42 is 7.
How to Find HCF of 455 and 42?
There are three methods to find the HCF of 455 and 42:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 455 and 42 by Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 455 and 42 can be expressed as:
455 = 5 x 7 x 13
42 = 2 x 3 x 7
The only common prime factor is 7.
Hence, HCF (455, 42) = 7.
HCF of 455 and 42 by Long Division Method
In the Long Division method, the below steps are followed.
- From the given set of numbers, the smallest number becomes the divisor, and the larger number becomes the dividend.
- In the next step, the smaller number becomes the dividend, and the remainder becomes the divisor.
- The above step is followed until the remainder is zero.
- The last divisor would be the HCF.
For 455 and 42, the HCF by long division method is:
Hence, HCF (455, 42) = 7
HCF of 455 and 42 by Listing Common Factors
By listing all the factors of given numbers, we can identify the Highest/Greatest/Biggest common factor, which is the HCF. Below is the list of factors for 455 and 42:
Factors of 455: 1, 5, 7, 13, 35, 65, 91, 455
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Therefore, HCF (455, 42) = 7
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Video Lesson on Properties of HCF and LCM
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Solved Examples
1. Find the second greatest number that divides 455 and 42.
The second greatest number that divides 455 and 42 evenly is 1.
2. What is the GCF of 42 and 84?
The GCF of 42 and 84 is 42.
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