The HCF of 84 and 90 is 6. The Highest Common Factor (HCF) of two or more numbers is defined as the largest number that is a factor of all the numbers. Students who are seeking the best material to obtain proficiency in the HCF concept can make use of Highest Common Factor
prepared by BYJU’S expert faculty. Using this article on a regular basis, students improve their skills in solving problems with speed and correctness. Learn the simple process of how to find the Highest Common Factor of 84 and 90 using prime factorisation, long division method and listing common factors in this article.
What is the HCF of 84 and 90?
The Highest Common Factor of 84 and 90 is 6. The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84, and the factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. The number 6 is the largest number that divides 84 and 90 completely.
How to Find HCF of 84 and 90?
Following are the three methods to find the HCF of 84 and 90:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 84 and 90 by Prime Factorisation Method
We write the given numbers as the product of prime factors in the prime factorisation method. To find the Highest Common Factor, multiply all the common prime factors with the lowest degree (power).
84 = 2 × 2 × 3 × 7
90 = 2 × 3 × 3 × 5
The common prime factors of 84 and 90 are 2 and 3.
Therefore,
HCF of (84, 90) = 2 × 3 = 6
HCF of 84 and 90 by Long Division Method
The steps mentioned below are used to find the Highest Common Factor of 84 and 90.
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 as zero. The last divisor will be the HCF of the given two numbers.
The HCF of 84 and 90 by the long division method is shown below:
HCF (84, 90) = 6
HCF of 84 and 90 by Listing Common Factors
In this method, we list out all the factors of given numbers to find the Highest Common Factor. The factors of 84 and 90 are given below:
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Hence, HCF (84, 90) = 6
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Video Lesson on Properties of HCF and LCM
Solved Examples
1. The product of two numbers is 7560. Find the LCM if their HCF is 6.
Solution: Given
HCF = 6
Product of numbers = 7560
We know that
LCM × HCF = Product of numbers
LCM × 6 = 7560
LCM = 1260
Therefore, the LCM is 1260.
2. Determine the highest number that divides 84 and 90 exactly.
Solution: The largest number that divides 84 and 90 exactly is their Highest Common Factor (HCF). The factors of 84 and 90 are as follows:
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Here, the HCF of 84 and 90 is 6. Hence, the largest number that divides 84 and 90 exactly is 6.
Frequently Asked Questions on HCF of 84 and 90
Mention the HCF of 84 and 90.
Name the methods to find the HCF of 84 and 90.
There are three methods to find the HCF of 84 and 90. They are as follows:
Prime Factorisation
Long Division Method
Listing Common Factors
9 is the HCF of 84 and 90. True or False.
Find the LCM if the HCF of 84 and 90 is 6.
We know that
HCF × LCM = 84 × 90
Given
HCF = 6
6 × LCM = 84 × 90
LCM = 1260
Hence, the LCM is 1260.
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