The HCF of 36 and 84 is 12. The greatest integer that can divide 36 and 84 evenly is defined as the Highest Common Factor (HCF) of 36 and 84. For a better understanding of the HCF, refer to the article HCF of Two Numbers anytime. Prime factorisation, the long division method and a list of common factors are the three commonly used methods to find the HCF of two numbers. Let us understand the simple method of finding the Highest Common Factor of 36 and 84, along with solved examples and FAQs in this article.
What is the HCF of 36 and 84?
The Highest Common Factor of 36 and 84 is 12. The largest positive integer that divides 36 and 84 exactly without any remainder is known as the Highest Common Factor of 36 and 84.
How to Find HCF of 36 and 84?
There are three methods to find the HCF of 36 and 84:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 36 and 84 by Prime Factorisation Method
In the prime factorisation, to find the HCF, we express the given numbers as the product of prime factors. Hence, 36 and 84 can be expressed as;
36 = 2 × 2 × 3 × 3
84 = 2 × 2 × 3 × 7
Common prime factors of 36 and 84 are 2, 2 and 3.
Therefore,
HCF (36, 84) = 2 × 2 × 3 = 12
HCF of 36 and 84 by Long Division Method
We can determine the HCF of 36 and 84 by using the following steps:
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 0, then make it a new divisor and write the previous divisor as the new dividend. Then perform the division.
Step 3: Continue this process until we get the remainder as zero. The last divisor will be the HCF of the given two numbers.
For 36 and 84, the HCF by long division method is;
HCF (36, 84) = 12
HCF of 36 and 84 by Listing the Factors
In this method, we find the HCF of 36 and 84 by listing out the common factors. The factors of 36 and 84 are given below:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Therefore, HCF (36, 84) = 12
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Video Lesson on Properties of HCF and LCM
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Solved Example
Question: What is the HCF of 36 and 84 if their LCM is 252?
Solution: Given,
LCM = 252
We know that,
LCM × HCF = 36 × 84
HCF (36, 84) = (36 × 84)/LCM
HCF (36, 84) = (36 × 84)/252
HCF (36, 84) = 12
Hence the Highest Common Factor of 36 and 84 is 12.
Frequently Asked Questions on HCF of 36 and 84
What is the HCF of 36 and 84?
Is the HCF of 36 and 84 the same as the HCF of 24 and 36?
Which of the following is the HCF of 36 and 84? 15, 19, 12, 20.
Name the methods to find the HCF of 36 and 84.
The following methods are used to find the HCF of 36 and 84
Prime Factorisation
Long Division method
Listing common factors
Find the HCF of 36 and 84 using prime factorisation.
In this method, we express the numbers as the product of prime factors
36 = 2 × 2 × 3 × 3
84 = 2 × 2 × 3 × 7
Common prime factors of 36 and 84 are 2, 2 and 3.
Therefore,
HCF (36, 84) = 2 × 2 × 3 = 12
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