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HCF of 24 and 90

HCF of 24 and 90 is the largest possible number that divides 24 and 90 exactly without any remainder. The factors of 24 and 90 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 respectively. There are 3 commonly used methods to find the HCF of 24 and 90 - prime factorization, long division, and Euclidean algorithm.

1.	HCF of 24 and 90
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 24 and 90?

Answer: HCF of 24 and 90 is 6.

Explanation:

The HCF of two non-zero integers, x(24) and y(90), is the highest positive integer m(6) that divides both x(24) and y(90) without any remainder.

Methods to Find HCF of 24 and 90

Let's look at the different methods for finding the HCF of 24 and 90.

Listing Common Factors
Prime Factorization Method
Long Division Method

HCF of 24 and 90 by Listing Common Factors

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

There are 4 common factors of 24 and 90, that are 1, 2, 3, and 6. Therefore, the highest common factor of 24 and 90 is 6.

HCF of 24 and 90 by Prime Factorization

Prime factorization of 24 and 90 is (2 × 2 × 2 × 3) and (2 × 3 × 3 × 5) respectively. As visible, 24 and 90 have common prime factors. Hence, the HCF of 24 and 90 is 2 × 3 = 6.

HCF of 24 and 90 by Long Division

HCF of 24 and 90 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 90 (larger number) by 24 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (18).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the HCF of 24 and 90.

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HCF of 24 and 90 Examples

Example 1: Find the highest number that divides 24 and 90 exactly.

Solution:

The highest number that divides 24 and 90 exactly is their highest common factor, i.e. HCF of 24 and 90.
⇒ Factors of 24 and 90:
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Therefore, the HCF of 24 and 90 is 6.
Example 2: Find the HCF of 24 and 90, if their LCM is 360.

Solution:

∵ LCM × HCF = 24 × 90
⇒ HCF(24, 90) = (24 × 90)/360 = 6
Therefore, the highest common factor of 24 and 90 is 6.
Example 3: The product of two numbers is 2160. If their HCF is 6, what is their LCM?

Solution:

Given: HCF = 6 and product of numbers = 2160
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 2160/6
Therefore, the LCM is 360.

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FAQs on HCF of 24 and 90

What is the HCF of 24 and 90?

The HCF of 24 and 90 is 6. To calculate the Highest common factor (HCF) of 24 and 90, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90) and choose the highest factor that exactly divides both 24 and 90, i.e., 6.

What are the Methods to Find HCF of 24 and 90?

There are three commonly used methods to find the HCF of 24 and 90.

By Prime Factorization
By Euclidean Algorithm
By Long Division

If the HCF of 90 and 24 is 6, Find its LCM.

HCF(90, 24) × LCM(90, 24) = 90 × 24
Since the HCF of 90 and 24 = 6
⇒ 6 × LCM(90, 24) = 2160
Therefore, LCM = 360
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How to Find the HCF of 24 and 90 by Long Division Method?

To find the HCF of 24, 90 using long division method, 90 is divided by 24. The corresponding divisor (6) when remainder equals 0 is taken as HCF.

What is the Relation Between LCM and HCF of 24, 90?

The following equation can be used to express the relation between LCM and HCF of 24 and 90, i.e. HCF × LCM = 24 × 90.

How to Find the HCF of 24 and 90 by Prime Factorization?

To find the HCF of 24 and 90, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 90 = 2 × 3 × 3 × 5.
⇒ Since 2, 3 are common terms in the prime factorization of 24 and 90. Hence, HCF(24, 90) = 2 × 3 = 6
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