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HCF of 24 and 25

HCF of 24 and 25 is the largest possible number that divides 24 and 25 exactly without any remainder. The factors of 24 and 25 are 1, 2, 3, 4, 6, 8, 12, 24 and 1, 5, 25 respectively. There are 3 commonly used methods to find the HCF of 24 and 25 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 24 and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 24 and 25?

Answer: HCF of 24 and 25 is 1.

Explanation:

The HCF of two non-zero integers, x(24) and y(25), is the highest positive integer m(1) that divides both x(24) and y(25) without any remainder.

Methods to Find HCF of 24 and 25

Let's look at the different methods for finding the HCF of 24 and 25.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

HCF of 24 and 25 by Prime Factorization

Prime factorization of 24 and 25 is (2 × 2 × 2 × 3) and (5 × 5) respectively. As visible, there are no common prime factors between 24 and 25, i.e. they are coprime. Hence, the HCF of 24 and 25 will be 1.

HCF of 24 and 25 by Long Division

HCF of 24 and 25 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 25 (larger number) by 24 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (24) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the HCF of 24 and 25.

HCF of 24 and 25 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 = 25 and Y = 24

HCF(25, 24) = HCF(24, 25 mod 24) = HCF(24, 1)
HCF(24, 1) = HCF(1, 24 mod 1) = HCF(1, 0)
HCF(1, 0) = 1 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 24 and 25 is 1.

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HCF of 24 and 25 Examples

Example 1: Find the HCF of 24 and 25, if their LCM is 600.

Solution:

∵ LCM × HCF = 24 × 25
⇒ HCF(24, 25) = (24 × 25)/600 = 1
Therefore, the highest common factor of 24 and 25 is 1.
Example 2: Find the highest number that divides 24 and 25 exactly.

Solution:

The highest number that divides 24 and 25 exactly is their highest common factor, i.e. HCF of 24 and 25.
⇒ Factors of 24 and 25:
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 25 = 1, 5, 25
Therefore, the HCF of 24 and 25 is 1.
Example 3: For two numbers, HCF = 1 and LCM = 600. If one number is 25, find the other number.

Solution:

Given: HCF (x, 25) = 1 and LCM (x, 25) = 600
∵ HCF × LCM = 25 × (x)
⇒ x = (HCF × LCM)/25
⇒ x = (1 × 600)/25
⇒ x = 24
Therefore, the other number is 24.

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FAQs on HCF of 24 and 25

What is the HCF of 24 and 25?

The HCF of 24 and 25 is 1. To calculate the HCF (Highest Common Factor) of 24 and 25, we need to factor each number (factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24; factors of 25 = 1, 5, 25) and choose the highest factor that exactly divides both 24 and 25, i.e., 1.

What is the Relation Between LCM and HCF of 24, 25?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 24 and 25, i.e. HCF × LCM = 24 × 25.

If the HCF of 25 and 24 is 1, Find its LCM.

HCF(25, 24) × LCM(25, 24) = 25 × 24
Since the HCF of 25 and 24 = 1
⇒ 1 × LCM(25, 24) = 600
Therefore, LCM = 600
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What are the Methods to Find HCF of 24 and 25?

There are three commonly used methods to find the HCF of 24 and 25.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the HCF of 24 and 25 by Long Division Method?

To find the HCF of 24, 25 using long division method, 25 is divided by 24. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

How to Find the HCF of 24 and 25 by Prime Factorization?

To find the HCF of 24 and 25, we will find the prime factorization of the given numbers, i.e. 24 = 2 × 2 × 2 × 3; 25 = 5 × 5.
⇒ There is no common prime factor for 24 and 25. Hence, HCF (24, 25) = 1.
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