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HCF of 18 and 24

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

1.	HCF of 18 and 24
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 18 and 24?

Answer: HCF of 18 and 24 is 6.

Explanation:

The HCF of two non-zero integers, x(18) and y(24), is the highest positive integer m(6) that divides both x(18) and y(24) without any remainder.

Methods to Find HCF of 18 and 24

Let's look at the different methods for finding the HCF of 18 and 24.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

HCF of 18 and 24 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 = 24 and Y = 18

HCF(24, 18) = HCF(18, 24 mod 18) = HCF(18, 6)
HCF(18, 6) = HCF(6, 18 mod 6) = HCF(6, 0)
HCF(6, 0) = 6 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 18 and 24 is 6.

HCF of 18 and 24 by Prime Factorization

Prime factorization of 18 and 24 is (2 × 3 × 3) and (2 × 2 × 2 × 3) respectively. As visible, 18 and 24 have common prime factors. Hence, the HCF of 18 and 24 is 2 × 3 = 6.

HCF of 18 and 24 by Long Division

HCF of 18 and 24 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 24 (larger number) by 18 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the HCF of 18 and 24.

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HCF of 18 and 24 Examples

Example 1: Find the highest number that divides 18 and 24 exactly.

Solution:

The highest number that divides 18 and 24 exactly is their highest common factor, i.e. HCF of 18 and 24.
⇒ Factors of 18 and 24:
- Factors of 18 = 1, 2, 3, 6, 9, 18
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Therefore, the HCF of 18 and 24 is 6.
Example 2: For two numbers, HCF = 6 and LCM = 72. If one number is 24, find the other number.

Solution:

Given: HCF (y, 24) = 6 and LCM (y, 24) = 72
∵ HCF × LCM = 24 × (y)
⇒ y = (HCF × LCM)/24
⇒ y = (6 × 72)/24
⇒ y = 18
Therefore, the other number is 18.
Example 3: Find the HCF of 18 and 24, if their LCM is 72.

Solution:

∵ LCM × HCF = 18 × 24
⇒ HCF(18, 24) = (18 × 24)/72 = 6
Therefore, the highest common factor of 18 and 24 is 6.

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FAQs on HCF of 18 and 24

What is the HCF of 18 and 24?

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

What is the Relation Between LCM and HCF of 18, 24?

The following equation can be used to express the relation between Least Common Multiple and HCF of 18 and 24, i.e. HCF × LCM = 18 × 24.

If the HCF of 24 and 18 is 6, Find its LCM.

HCF(24, 18) × LCM(24, 18) = 24 × 18
Since the HCF of 24 and 18 = 6
⇒ 6 × LCM(24, 18) = 432
Therefore, LCM = 72
☛ Highest Common Factor Calculator

How to Find the HCF of 18 and 24 by Long Division Method?

To find the HCF of 18, 24 using long division method, 24 is divided by 18. The corresponding divisor (6) when remainder equals 0 is taken as HCF.

What are the Methods to Find HCF of 18 and 24?

There are three commonly used methods to find the HCF of 18 and 24.

By Euclidean Algorithm
By Long Division
By Prime Factorization

How to Find the HCF of 18 and 24 by Prime Factorization?

To find the HCF of 18 and 24, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 24 = 2 × 2 × 2 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 18 and 24. Hence, HCF(18, 24) = 2 × 3 = 6
☛ What is a Prime Number?

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