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HCF of 2, 3 and 4

HCF of 2, 3 and 4 is the largest possible number that divides 2, 3 and 4 exactly without any remainder. The factors of 2, 3 and 4 are (1, 2), (1, 3) and (1, 2, 4) respectively. There are 3 commonly used methods to find the HCF of 2, 3 and 4 - prime factorization, Euclidean algorithm, and long division.

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

What is HCF of 2, 3 and 4?

Answer: HCF of 2, 3 and 4 is 1.

Explanation:

The HCF of three non-zero integers, x(2), y(3) and z(4), is the highest positive integer m(1) that divides x(2), y(3) and z(4) without any remainder.

Methods to Find HCF of 2, 3 and 4

The methods to find the HCF of 2, 3 and 4 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

HCF of 2, 3 and 4 by Prime Factorization

Prime factorization of 2, 3 and 4 is (2), (3) and (2 × 2) respectively. As visible, there are no common prime factors between 2, 3 and 4, i.e. they are co-prime. Hence, the HCF of 2, 3 and 4 will be 1.

HCF of 2, 3 and 4 by Long Division

HCF of 2, 3 and 4 can be represented as HCF of (HCF of 2, 3) and 4. HCF(2, 3, 4) can be thus calculated by first finding HCF(2, 3) using long division and thereafter using this result with 4 to perform long division again.

Step 1: Divide 3 (larger number) by 2 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (2) by the remainder (1). Repeat this process until the remainder = 0.
⇒ HCF(2, 3) = 1.
Step 3: Now to find the HCF of 1 and 4, we will perform a long division on 4 and 1.
Step 4: For remainder = 0, divisor = 1 ⇒ HCF(1, 4) = 1

Thus, HCF(2, 3, 4) = HCF(HCF(2, 3), 4) = 1.

HCF of 2, 3 and 4 by Listing Common Factors

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

Since, 1 is the only common factor between 2, 3 and 4. The Highest Common Factor of 2, 3 and 4 is 1.

☛ Also Check:

HCF of 2, 3 and 4 Examples

Example 1: Verify the relation between the LCM and HCF of 2, 3 and 4.

Solution:

The relation between the LCM and HCF of 2, 3 and 4 is given as, HCF(2, 3, 4) = [(2 × 3 × 4) × LCM(2, 3, 4)]/[LCM(2, 3) × LCM (3, 4) × LCM(2, 4)]
⇒ Prime factorization of 2, 3 and 4:
- 2 = 2
- 3 = 3
- 4 = 2 × 2
∴ LCM of (2, 3), (3, 4), (2, 4), and (2, 3, 4) is 6, 12, 4, and 12 respectively.
Now, LHS = HCF(2, 3, 4) = 1.
And, RHS = [(2 × 3 × 4) × LCM(2, 3, 4)]/[LCM(2, 3) × LCM (3, 4) × LCM(2, 4)] = [(24) × 12]/[6 × 12 × 4]
LHS = RHS = 1.
Hence verified.
Example 2: Calculate the HCF of 2, 3, and 4 using LCM of the given numbers.

Solution:

Prime factorization of 2, 3 and 4 is given as,
- 2 = 2
- 3 = 3
- 4 = 2 × 2
LCM(2, 3) = 6, LCM(3, 4) = 12, LCM(4, 2) = 4, LCM(2, 3, 4) = 12
⇒ HCF(2, 3, 4) = [(2 × 3 × 4) × LCM(2, 3, 4)]/[LCM(2, 3) × LCM (3, 4) × LCM(4, 2)]
⇒ HCF(2, 3, 4) = (24 × 12)/(6 × 12 × 4)
⇒ HCF(2, 3, 4) = 1.
Therefore, the HCF of 2, 3 and 4 is 1.
Example 3: Find the highest number that divides 2, 3, and 4 completely.

Solution:

The highest number that divides 2, 3, and 4 exactly is their highest common factor.
- Factors of 2 = 1, 2
- Factors of 3 = 1, 3
- Factors of 4 = 1, 2, 4
The HCF of 2, 3, and 4 is 1.
∴ The highest number that divides 2, 3, and 4 is 1.

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FAQs on HCF of 2, 3 and 4

What is the HCF of 2, 3 and 4?

The HCF of 2, 3 and 4 is 1. To calculate the highest common factor of 2, 3 and 4, we need to factor each number (factors of 2 = 1, 2; factors of 3 = 1, 3; factors of 4 = 1, 2, 4) and choose the highest factor that exactly divides 2, 3 and 4, i.e., 1.

What are the Methods to Find HCF of 2, 3 and 4?

There are three commonly used methods to find the HCF of 2, 3 and 4.

By Long Division
By Prime Factorization
By Euclidean Algorithm

Which of the following is HCF of 2, 3 and 4? 1, 37, 43, 24, 42, 5

HCF of 2, 3, 4 will be the number that divides 2, 3, and 4 without leaving any remainder. The only number that satisfies the given condition is 1.

How to Find the HCF of 2, 3 and 4 by Prime Factorization?

To find the HCF of 2, 3 and 4, we will find the prime factorization of given numbers, i.e. 2 = 2; 3 = 3; 4 = 2 × 2.
⇒ There is no common prime factor for 2, 3 and 4. Hence, HCF(2, 3, 4) = 1.
☛ Prime Number

What is the Relation Between LCM and HCF of 2, 3 and 4?

The following equation can be used to express the relation between Least Common Multiple and HCF of 2, 3 and 4, i.e. HCF(2, 3, 4) = [(2 × 3 × 4) × LCM(2, 3, 4)]/[LCM(2, 3) × LCM (3, 4) × LCM(2, 4)].
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