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HCF of 28 and 36

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

1.	HCF of 28 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 28 and 36?

Answer: HCF of 28 and 36 is 4.

Explanation:

The HCF of two non-zero integers, x(28) and y(36), is the highest positive integer m(4) that divides both x(28) and y(36) without any remainder.

Methods to Find HCF of 28 and 36

Let's look at the different methods for finding the HCF of 28 and 36.

Long Division Method
Listing Common Factors
Prime Factorization Method

HCF of 28 and 36 by Long Division

HCF of 28 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 36 (larger number) by 28 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (28) by the remainder (8).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the HCF of 28 and 36.

HCF of 28 and 36 by Listing Common Factors

Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

There are 3 common factors of 28 and 36, that are 1, 2, and 4. Therefore, the highest common factor of 28 and 36 is 4.

HCF of 28 and 36 by Prime Factorization

Prime factorization of 28 and 36 is (2 × 2 × 7) and (2 × 2 × 3 × 3) respectively. As visible, 28 and 36 have common prime factors. Hence, the HCF of 28 and 36 is 2 × 2 = 4.

☛ Also Check:

HCF of 28 and 36 Examples

Example 1: Find the HCF of 28 and 36, if their LCM is 252.

Solution:

∵ LCM × HCF = 28 × 36
⇒ HCF(28, 36) = (28 × 36)/252 = 4
Therefore, the highest common factor of 28 and 36 is 4.
Example 2: Find the highest number that divides 28 and 36 exactly.

Solution:

The highest number that divides 28 and 36 exactly is their highest common factor, i.e. HCF of 28 and 36.
⇒ Factors of 28 and 36:
- Factors of 28 = 1, 2, 4, 7, 14, 28
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Therefore, the HCF of 28 and 36 is 4.
Example 3: For two numbers, HCF = 4 and LCM = 252. If one number is 36, find the other number.

Solution:

Given: HCF (z, 36) = 4 and LCM (z, 36) = 252
∵ HCF × LCM = 36 × (z)
⇒ z = (HCF × LCM)/36
⇒ z = (4 × 252)/36
⇒ z = 28
Therefore, the other number is 28.

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FAQs on HCF of 28 and 36

What is the HCF of 28 and 36?

The HCF of 28 and 36 is 4. To calculate the Highest common factor of 28 and 36, we need to factor each number (factors of 28 = 1, 2, 4, 7, 14, 28; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the highest factor that exactly divides both 28 and 36, i.e., 4.

How to Find the HCF of 28 and 36 by Long Division Method?

To find the HCF of 28, 36 using long division method, 36 is divided by 28. The corresponding divisor (4) when remainder equals 0 is taken as HCF.

How to Find the HCF of 28 and 36 by Prime Factorization?

To find the HCF of 28 and 36, we will find the prime factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 36 = 2 × 2 × 3 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 28 and 36. Hence, HCF(28, 36) = 2 × 2 = 4
☛ What is a Prime Number?

If the HCF of 36 and 28 is 4, Find its LCM.

HCF(36, 28) × LCM(36, 28) = 36 × 28
Since the HCF of 36 and 28 = 4
⇒ 4 × LCM(36, 28) = 1008
Therefore, LCM = 252
☛ HCF Calculator

What are the Methods to Find HCF of 28 and 36?

There are three commonly used methods to find the HCF of 28 and 36.

By Euclidean Algorithm
By Prime Factorization
By Long Division

What is the Relation Between LCM and HCF of 28, 36?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 28 and 36, i.e. HCF × LCM = 28 × 36.

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