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HCF of 36 and 84

HCF of 36 and 84 is the largest possible number that divides 36 and 84 exactly without any remainder. The factors of 36 and 84 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 respectively. There are 3 commonly used methods to find the HCF of 36 and 84 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 36 and 84
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 36 and 84?

Answer: HCF of 36 and 84 is 12.

Explanation:

The HCF of two non-zero integers, x(36) and y(84), is the highest positive integer m(12) that divides both x(36) and y(84) without any remainder.

Methods to Find HCF of 36 and 84

The methods to find the HCF of 36 and 84 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

HCF of 36 and 84 by Long Division

HCF of 36 and 84 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 84 (larger number) by 36 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (12) is the HCF of 36 and 84.

HCF of 36 and 84 by Prime Factorization

Prime factorization of 36 and 84 is (2 × 2 × 3 × 3) and (2 × 2 × 3 × 7) respectively. As visible, 36 and 84 have common prime factors. Hence, the HCF of 36 and 84 is 2 × 2 × 3 = 12.

HCF of 36 and 84 by Euclidean Algorithm

As per the Euclidean Algorithm, HCF(X, Y) = HCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 84 and Y = 36

HCF(84, 36) = HCF(36, 84 mod 36) = HCF(36, 12)
HCF(36, 12) = HCF(12, 36 mod 12) = HCF(12, 0)
HCF(12, 0) = 12 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 36 and 84 is 12.

☛ Also Check:

HCF of 36 and 84 Examples

Example 1: The product of two numbers is 3024. If their HCF is 12, what is their LCM?

Solution:

Given: HCF = 12 and product of numbers = 3024
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 3024/12
Therefore, the LCM is 252.
Example 2: For two numbers, HCF = 12 and LCM = 252. If one number is 36, find the other number.

Solution:

Given: HCF (z, 36) = 12 and LCM (z, 36) = 252
∵ HCF × LCM = 36 × (z)
⇒ z = (HCF × LCM)/36
⇒ z = (12 × 252)/36
⇒ z = 84
Therefore, the other number is 84.
Example 3: Find the HCF of 36 and 84, if their LCM is 252.

Solution:

∵ LCM × HCF = 36 × 84
⇒ HCF(36, 84) = (36 × 84)/252 = 12
Therefore, the highest common factor of 36 and 84 is 12.

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FAQs on HCF of 36 and 84

What is the HCF of 36 and 84?

The HCF of 36 and 84 is 12. To calculate the HCF (Highest Common Factor) of 36 and 84, we need to factor each number (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) and choose the highest factor that exactly divides both 36 and 84, i.e., 12.

How to Find the HCF of 36 and 84 by Prime Factorization?

To find the HCF of 36 and 84, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 84 = 2 × 2 × 3 × 7.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 36 and 84. Hence, HCF(36, 84) = 2 × 2 × 3 = 12
☛ Prime Number

How to Find the HCF of 36 and 84 by Long Division Method?

To find the HCF of 36, 84 using long division method, 84 is divided by 36. The corresponding divisor (12) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 36, 84?

The following equation can be used to express the relation between Least Common Multiple and HCF of 36 and 84, i.e. HCF × LCM = 36 × 84.

What are the Methods to Find HCF of 36 and 84?

There are three commonly used methods to find the HCF of 36 and 84.

By Prime Factorization
By Listing Common Factors
By Long Division

If the HCF of 84 and 36 is 12, Find its LCM.

HCF(84, 36) × LCM(84, 36) = 84 × 36
Since the HCF of 84 and 36 = 12
⇒ 12 × LCM(84, 36) = 3024
Therefore, LCM = 252
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