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HCF of 24, 36 and 40

HCF of 24, 36 and 40 is the largest possible number that divides 24, 36 and 40 exactly without any remainder. The factors of 24, 36 and 40 are (1, 2, 3, 4, 6, 8, 12, 24), (1, 2, 3, 4, 6, 9, 12, 18, 36) and (1, 2, 4, 5, 8, 10, 20, 40) respectively. There are 3 commonly used methods to find the HCF of 24, 36 and 40 - Euclidean algorithm, long division, and prime factorization.

1.	HCF of 24, 36 and 40
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 24, 36 and 40?

Answer: HCF of 24, 36 and 40 is 4.

Explanation:

The HCF of three non-zero integers, x(24), y(36) and z(40), is the highest positive integer m(4) that divides x(24), y(36) and z(40) without any remainder.

Methods to Find HCF of 24, 36 and 40

The methods to find the HCF of 24, 36 and 40 are explained below.

Prime Factorization Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 24, 36 and 40 by Prime Factorization

Prime factorization of 24, 36 and 40 is (2 × 2 × 2 × 3), (2 × 2 × 3 × 3) and (2 × 2 × 2 × 5) respectively. As visible, 24, 36 and 40 have common prime factors. Hence, the HCF of 24, 36 and 40 is 2 × 2 = 4.

HCF of 24, 36 and 40 by Listing Common Factors

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

There are 3 common factors of 24, 36 and 40, that are 1, 2, and 4. Therefore, the highest common factor of 24, 36 and 40 is 4.

HCF of 24, 36 and 40 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(24, 36, 40) = HCF(HCF(24, 36), 40)

HCF(36, 24) = HCF(24, 36 mod 24) = HCF(24, 12)
HCF(24, 12) = HCF(12, 24 mod 12) = HCF(12, 0)
HCF(12, 0) = 12 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Steps for HCF(12, 40)

HCF(40, 12) = HCF(12, 40 mod 12) = HCF(12, 4)
HCF(12, 4) = HCF(4, 12 mod 4) = HCF(4, 0)
HCF(4, 0) = 4 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 24, 36 and 40 is 4.

☛ Also Check:

HCF of 24, 36 and 40 Examples

Example 1: Calculate the HCF of 24, 36, and 40 using LCM of the given numbers.

Solution:

Prime factorization of 24, 36 and 40 is given as,
- 24 = 2 × 2 × 2 × 3
- 36 = 2 × 2 × 3 × 3
- 40 = 2 × 2 × 2 × 5
LCM(24, 36) = 72, LCM(36, 40) = 360, LCM(40, 24) = 120, LCM(24, 36, 40) = 360
⇒ HCF(24, 36, 40) = [(24 × 36 × 40) × LCM(24, 36, 40)]/[LCM(24, 36) × LCM (36, 40) × LCM(40, 24)]
⇒ HCF(24, 36, 40) = (34560 × 360)/(72 × 360 × 120)
⇒ HCF(24, 36, 40) = 4.
Therefore, the HCF of 24, 36 and 40 is 4.
Example 2: Verify the relation between the LCM and HCF of 24, 36 and 40.

Solution:

The relation between the LCM and HCF of 24, 36 and 40 is given as, HCF(24, 36, 40) = [(24 × 36 × 40) × LCM(24, 36, 40)]/[LCM(24, 36) × LCM (36, 40) × LCM(24, 40)]
⇒ Prime factorization of 24, 36 and 40:
- 24 = 2 × 2 × 2 × 3
- 36 = 2 × 2 × 3 × 3
- 40 = 2 × 2 × 2 × 5
∴ LCM of (24, 36), (36, 40), (24, 40), and (24, 36, 40) is 72, 360, 120, and 360 respectively.
Now, LHS = HCF(24, 36, 40) = 4.
And, RHS = [(24 × 36 × 40) × LCM(24, 36, 40)]/[LCM(24, 36) × LCM (36, 40) × LCM(24, 40)] = [(34560) × 360]/[72 × 360 × 120]
LHS = RHS = 4.
Hence verified.
Example 3: Find the highest number that divides 24, 36, and 40 completely.

Solution:

The highest number that divides 24, 36, and 40 exactly is their highest common factor.
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
The HCF of 24, 36, and 40 is 4.
∴ The highest number that divides 24, 36, and 40 is 4.

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FAQs on HCF of 24, 36 and 40

What is the HCF of 24, 36 and 40?

The HCF of 24, 36 and 40 is 4. To calculate the highest common factor of 24, 36 and 40, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the highest factor that exactly divides 24, 36 and 40, i.e., 4.

What are the Methods to Find HCF of 24, 36 and 40?

There are three commonly used methods to find the HCF of 24, 36 and 40.

By Long Division
By Listing Common Factors
By Prime Factorization

What is the Relation Between LCM and HCF of 24, 36 and 40?

The following equation can be used to express the relation between LCM and HCF of 24, 36 and 40, i.e. HCF(24, 36, 40) = [(24 × 36 × 40) × LCM(24, 36, 40)]/[LCM(24, 36) × LCM (36, 40) × LCM(24, 40)].
☛ Highest Common Factor Calculator

Which of the following is HCF of 24, 36 and 40? 4, 87, 88, 57, 60, 46, 67, 70

HCF of 24, 36, 40 will be the number that divides 24, 36, and 40 without leaving any remainder. The only number that satisfies the given condition is 4.

How to Find the HCF of 24, 36 and 40 by Prime Factorization?

To find the HCF of 24, 36 and 40, we will find the prime factorization of given numbers, i.e. 24 = 2 × 2 × 2 × 3; 36 = 2 × 2 × 3 × 3; 40 = 2 × 2 × 2 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 24, 36 and 40. Hence, HCF(24, 36, 40) = 2 × 2 = 4
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