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HCF of 36 and 48

HCF of 36 and 48 is the largest possible number that divides 36 and 48 exactly without any remainder. The factors of 36 and 48 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There are 3 commonly used methods to find the HCF of 36 and 48 - long division, prime factorization, and Euclidean algorithm.

1.	HCF of 36 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 36 and 48?

Answer: HCF of 36 and 48 is 12.

Explanation:

The HCF of two non-zero integers, x(36) and y(48), is the highest positive integer m(12) that divides both x(36) and y(48) without any remainder.

Methods to Find HCF of 36 and 48

Let's look at the different methods for finding the HCF of 36 and 48.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

HCF of 36 and 48 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 = 48 and Y = 36

HCF(48, 36) = HCF(36, 48 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 48 is 12.

HCF of 36 and 48 by Prime Factorization

Prime factorization of 36 and 48 is (2 × 2 × 3 × 3) and (2 × 2 × 2 × 2 × 3) respectively. As visible, 36 and 48 have common prime factors. Hence, the HCF of 36 and 48 is 2 × 2 × 3 = 12.

HCF of 36 and 48 by Long Division

HCF of 36 and 48 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 48 (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 48.

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HCF of 36 and 48 Examples

Example 1: The product of two numbers is 1728. If their HCF is 12, what is their LCM?

Solution:

Given: HCF = 12 and product of numbers = 1728
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 1728/12
Therefore, the LCM is 144.
Example 2: Find the highest number that divides 36 and 48 exactly.

Solution:

The highest number that divides 36 and 48 exactly is their highest common factor, i.e. HCF of 36 and 48.
⇒ Factors of 36 and 48:
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Therefore, the HCF of 36 and 48 is 12.
Example 3: For two numbers, HCF = 12 and LCM = 144. If one number is 36, find the other number.

Solution:

Given: HCF (z, 36) = 12 and LCM (z, 36) = 144
∵ HCF × LCM = 36 × (z)
⇒ z = (HCF × LCM)/36
⇒ z = (12 × 144)/36
⇒ z = 48
Therefore, the other number is 48.

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FAQs on HCF of 36 and 48

What is the HCF of 36 and 48?

The HCF of 36 and 48 is 12. To calculate the HCF (Highest Common Factor) of 36 and 48, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and choose the highest factor that exactly divides both 36 and 48, i.e., 12.

How to Find the HCF of 36 and 48 by Long Division Method?

To find the HCF of 36, 48 using long division method, 48 is divided by 36. The corresponding divisor (12) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 36 and 48?

There are three commonly used methods to find the HCF of 36 and 48.

By Prime Factorization
By Listing Common Factors
By Long Division

How to Find the HCF of 36 and 48 by Prime Factorization?

To find the HCF of 36 and 48, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 36 and 48. Hence, HCF(36, 48) = 2 × 2 × 3 = 12
☛ Prime Number

What is the Relation Between LCM and HCF of 36, 48?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 36 and 48, i.e. HCF × LCM = 36 × 48.

If the HCF of 48 and 36 is 12, Find its LCM.

HCF(48, 36) × LCM(48, 36) = 48 × 36
Since the HCF of 48 and 36 = 12
⇒ 12 × LCM(48, 36) = 1728
Therefore, LCM = 144
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