The HCF of 504 and 980 is 28. The number 28 is the largest number that divides 504 and 980 evenly. To learn more about HCF, students can follow the article Highest Common Factor formulated by BYJU’S experts. This article explains the simple way of finding the HCF of given numbers, along with clarifying the doubts of students immediately. Here, we will discuss the simple procedure of verifying the Highest Common Factor of 504 and 980 using prime factorisation, the long division method and listing common factors in a precise manner.
What is the HCF of 504 and 980?
The Highest Common Factor of 504 and 980 is 28. There are six common factors of 504 and 980. They are 1, 2, 4, 7, 14 and 28. Hence, the Highest Common Factor of 504 and 980 is 28.
How to Find HCF of 504 and 980?
There are three methods to find the HCF of 504 and 980:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 504 and 980 by Prime Factorisation Method
To find the HCF by prime factorisation method, we express the numbers as the product of prime factors. Hence, the given numbers 504 and 980 can be expressed as:
504 = 2 × 2 × 2 × 3 × 3 × 7
980 = 2 × 2 × 5 × 7 × 7
The common prime factors of 504 and 980 are 2, 2 and 7.
Therefore,
HCF (504, 980) = 2 × 2 × 7 = 28
HCF of 504 and 980 by Long Division Method
In the long division method, we use the below steps to determine the HCF of 504 and 980.
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 considered as the HCF of the given two numbers.
The HCF of 504 and 980 by long division method is:
HCF (504, 980) = 28
HCF of 504 and 980 by Listing Common Factors
In this method, we list out the factors of 504 and 980 to find their HCF. Check the factors of 504 and 980 given below.
Factors of 504:1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504
Factors of 980: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 49, 70, 98, 140, 196, 245, 490, 980
Hence, HCF (504, 980) = 28
Related Articles
Video Lesson on Properties of HCF and LCM
Solved Examples
1. What is the highest number that divides both 504 and 980 exactly?
Solution: The largest number that divides both 504 and 980 exactly is their Highest Common Factor (HCF). Here, the Highest Common Factor of 504 and 980 is 28. Hence, 28 is the highest number that divides both 504 and 980 exactly.
2. The product of two numbers is 493920. If their HCF is 28, what is their LCM?
Solution: Given
HCF = 28
Product of numbers = 493920
We know that
LCM × HCF = Product of numbers
LCM = Product of numbers/HCF
LCM = 493920/28
LCM = 17640
Hence, the LCM is 17640.
Frequently Asked Questions on HCF of 504 and 980
What is the HCF of 504 and 980?
How to find the HCF of 504 and 980 by prime factorisation?
In this method, we express the given numbers as the product of prime factors. Therefore, the numbers 504 and 980 can be expressed as:
504 = 2 × 2 × 2 × 3 × 3 × 7
980 = 2 × 2 × 5 × 7 × 7
HCF (504, 980) = 2 × 2 × 7 = 28
What are the common factors of 504 and 980?
Write the methods used to find the HCF of 504 and 980.
We can use the following methods to find the HCF of 504 and 980:
Prime Factorisation
Long Division method
Listing common factors
If the HCF of 504 and 980 is 28, what is their LCM?
We know that
HCF × LCM = 504 × 980
Given
HCF = 28
28 × LCM = 504 × 980
LCM = 17640
Hence, the LCM is 17640.
Comments