The HCF of 510 and 92 is 2. The highest number among all the common factors of given numbers is defined as the Highest Common Factor (HCF). Prime factorisation, long division method and listing of common factors are the three methods used to find the HCF of given numbers. Students can make use of the article Highest Common Factor prepared by subject experts at BYJU’S and clarify their doubts which arise while solving the problems based on the HCF. Let us glance at the simple procedure on how to find the Highest Common Factor of 510 and 92 with a complete explanation in this article.
What is the HCF of 510 and 92?
The Highest Common Factor (HCF) of 510 and 92 is 2. The factors of 92 are 1, 2, 4, 23, 46, 92 and the factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510. Among these factors, 2 is the Highest Common Factor of 510 and 92.
How to Find the HCF of 510 and 92?
There are three methods to find the HCF of 510 and 92:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 510 and 92 by Prime Factorisation Method
In the prime factorisation method, we express the numbers as the product of prime factors. To find the highest common factor, multiply all the common prime factors with the lowest degree (power).
510 = 2 × 3 × 5 × 17
92 = 2 × 2 × 23
Common prime factors of 510 and 92 are 2.
Therefore, HCF of (510, 92) = 2
HCF of 510 and 92 by Long Division Method
Follow the steps given below to find the Highest Common Factor of 510 and 92 using the long division method:
Step 1: Divide the largest number by the smallest among the given two numbers
Step 2: Check the remainder; if it is not zero, then make it a new divisor and mention the previous divisor as the new dividend and continue the division.
Step 3: Repeat this process until we get the remainder equal to zero. The last divisor is considered as the HCF of the given two numbers.
Let us look at the division method given below for a better understanding.
HCF (510, 92) = 2
HCF of 510 and 92 by Listing the Factors
In this method, we need to list out the common factors of 510 and 92 and pick up the largest among them.
Factors of 510: 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
Factors of 92: 1, 2, 4, 23, 46, 92
Therefore, HCF (510, 92) = 2
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Video Lesson on Properties of HCF and LCM
Solved Example
Question: What is the highest number that divides 510 and 92 exactly?
Solution: The highest number that divides numbers 510 and 92 exactly is their Highest Common Factor. The Highest Common Factor of 510 and 92 is 2. Therefore, 2 is the highest number that divides 510 and 92 exactly.
Frequently Asked Questions on HCF of 510 and 92
What is the HCF of 510 and 92?
List out the methods used to find the HCF of 510 and 92.
There are three methods to find the HCF of 510 and 92. They are as follows:
Prime Factorisation
Long Division Method
Listing Common Factors
What are the common prime factors of 510 and 92?
Find the LCM if the HCF of 510 and 92 is 2.
We know that
HCF × LCM = 510 × 92
Given
HCF = 2
2 × LCM = 510 × 92
LCM = 23460
Hence the LCM is 23460
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