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HCF of 12, 36 and 48

HCF of 12, 36 and 48 is the largest possible number that divides 12, 36 and 48 exactly without any remainder. The factors of 12, 36 and 48 are (1, 2, 3, 4, 6, 12), (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 12, 36 and 48 - Euclidean algorithm, prime factorization, and long division.

1.	HCF of 12, 36 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 12, 36 and 48?

Answer: HCF of 12, 36 and 48 is 12.

Explanation:

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

Methods to Find HCF of 12, 36 and 48

Let's look at the different methods for finding the HCF of 12, 36 and 48.

Using Euclid's Algorithm
Prime Factorization Method
Listing Common Factors

HCF of 12, 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.

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

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

Steps for HCF(12, 48)

HCF(48, 12) = HCF(12, 48 mod 12) = HCF(12, 0)
HCF(12, 0) = 12 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 12, 36 and 48 is 12.

HCF of 12, 36 and 48 by Prime Factorization

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

HCF of 12, 36 and 48 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12
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

There are 6 common factors of 12, 36 and 48, that are 1, 2, 3, 4, 6, and 12. Therefore, the highest common factor of 12, 36 and 48 is 12.

☛ Also Check:

HCF of 12, 36 and 48 Examples

Example 1: Verify the relation between the LCM and HCF of 12, 36 and 48.

Solution:

The relation between the LCM and HCF of 12, 36 and 48 is given as, HCF(12, 36, 48) = [(12 × 36 × 48) × LCM(12, 36, 48)]/[LCM(12, 36) × LCM (36, 48) × LCM(12, 48)]
⇒ Prime factorization of 12, 36 and 48:
- 12 = 2 × 2 × 3
- 36 = 2 × 2 × 3 × 3
- 48 = 2 × 2 × 2 × 2 × 3
∴ LCM of (12, 36), (36, 48), (12, 48), and (12, 36, 48) is 36, 144, 48, and 144 respectively.
Now, LHS = HCF(12, 36, 48) = 12.
And, RHS = [(12 × 36 × 48) × LCM(12, 36, 48)]/[LCM(12, 36) × LCM (36, 48) × LCM(12, 48)] = [(20736) × 144]/[36 × 144 × 48]
LHS = RHS = 12.
Hence verified.
Example 2: Find the highest number that divides 12, 36, and 48 completely.

Solution:

The highest number that divides 12, 36, and 48 exactly is their highest common factor.
- Factors of 12 = 1, 2, 3, 4, 6, 12
- 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
The HCF of 12, 36, and 48 is 12.
∴ The highest number that divides 12, 36, and 48 is 12.
Example 3: Calculate the HCF of 12, 36, and 48 using LCM of the given numbers.

Solution:

Prime factorization of 12, 36 and 48 is given as,
- 12 = 2 × 2 × 3
- 36 = 2 × 2 × 3 × 3
- 48 = 2 × 2 × 2 × 2 × 3
LCM(12, 36) = 36, LCM(36, 48) = 144, LCM(48, 12) = 48, LCM(12, 36, 48) = 144
⇒ HCF(12, 36, 48) = [(12 × 36 × 48) × LCM(12, 36, 48)]/[LCM(12, 36) × LCM (36, 48) × LCM(48, 12)]
⇒ HCF(12, 36, 48) = (20736 × 144)/(36 × 144 × 48)
⇒ HCF(12, 36, 48) = 12.
Therefore, the HCF of 12, 36 and 48 is 12.

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FAQs on HCF of 12, 36 and 48

What is the HCF of 12, 36 and 48?

The HCF of 12, 36 and 48 is 12. To calculate the highest common factor of 12, 36 and 48, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; 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 12, 36 and 48, i.e., 12.

How to Find the HCF of 12, 36 and 48 by Prime Factorization?

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

What are the Methods to Find HCF of 12, 36 and 48?

There are three commonly used methods to find the HCF of 12, 36 and 48.

By Prime Factorization
By Long Division
By Listing Common Factors

Which of the following is HCF of 12, 36 and 48? 12, 89, 55, 63, 97, 55, 97

HCF of 12, 36, 48 will be the number that divides 12, 36, and 48 without leaving any remainder. The only number that satisfies the given condition is 12.

What is the Relation Between LCM and HCF of 12, 36 and 48?

The following equation can be used to express the relation between LCM and HCF of 12, 36 and 48, i.e. HCF(12, 36, 48) = [(12 × 36 × 48) × LCM(12, 36, 48)]/[LCM(12, 36) × LCM (36, 48) × LCM(12, 48)].
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