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HCF of 25 and 36

HCF of 25 and 36 is the largest possible number that divides 25 and 36 exactly without any remainder. The factors of 25 and 36 are 1, 5, 25 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There are 3 commonly used methods to find the HCF of 25 and 36 - long division, Euclidean algorithm, and prime factorization.

1.	HCF of 25 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 25 and 36?

Answer: HCF of 25 and 36 is 1.

Explanation:

The HCF of two non-zero integers, x(25) and y(36), is the highest positive integer m(1) that divides both x(25) and y(36) without any remainder.

Methods to Find HCF of 25 and 36

The methods to find the HCF of 25 and 36 are explained below.

Prime Factorization Method
Using Euclid's Algorithm
Long Division Method

HCF of 25 and 36 by Prime Factorization

Prime factorization of 25 and 36 is (5 × 5) and (2 × 2 × 3 × 3) respectively. As visible, there are no common prime factors between 25 and 36, i.e. they are co-prime. Hence, the HCF of 25 and 36 will be 1.

HCF of 25 and 36 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 = 36 and Y = 25

HCF(36, 25) = HCF(25, 36 mod 25) = HCF(25, 11)
HCF(25, 11) = HCF(11, 25 mod 11) = HCF(11, 3)
HCF(11, 3) = HCF(3, 11 mod 3) = HCF(3, 2)
HCF(3, 2) = HCF(2, 3 mod 2) = HCF(2, 1)
HCF(2, 1) = 1 (∵ HCF(X, 1) = 1)

Therefore, the value of HCF of 25 and 36 is 1.

HCF of 25 and 36 by Long Division

HCF of 25 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 36 (larger number) by 25 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (25) by the remainder (11).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the HCF of 25 and 36.

☛ Also Check:

HCF of 25 and 36 Examples

Example 1: For two numbers, HCF = 1 and LCM = 900. If one number is 36, find the other number.

Solution:

Given: HCF (z, 36) = 1 and LCM (z, 36) = 900
∵ HCF × LCM = 36 × (z)
⇒ z = (HCF × LCM)/36
⇒ z = (1 × 900)/36
⇒ z = 25
Therefore, the other number is 25.
Example 2: Find the HCF of 25 and 36, if their LCM is 900.

Solution:

∵ LCM × HCF = 25 × 36
⇒ HCF(25, 36) = (25 × 36)/900 = 1
Therefore, the highest common factor of 25 and 36 is 1.
Example 3: Find the highest number that divides 25 and 36 exactly.

Solution:

The highest number that divides 25 and 36 exactly is their highest common factor, i.e. HCF of 25 and 36.
⇒ Factors of 25 and 36:
- Factors of 25 = 1, 5, 25
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Therefore, the HCF of 25 and 36 is 1.

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FAQs on HCF of 25 and 36

What is the HCF of 25 and 36?

The HCF of 25 and 36 is 1. To calculate the Highest common factor of 25 and 36, we need to factor each number (factors of 25 = 1, 5, 25; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the highest factor that exactly divides both 25 and 36, i.e., 1.

How to Find the HCF of 25 and 36 by Long Division Method?

To find the HCF of 25, 36 using long division method, 36 is divided by 25. The corresponding divisor (1) when remainder equals 0 is taken as HCF.

How to Find the HCF of 25 and 36 by Prime Factorization?

To find the HCF of 25 and 36, we will find the prime factorization of the given numbers, i.e. 25 = 5 × 5; 36 = 2 × 2 × 3 × 3.
⇒ There is no common prime factor for 25 and 36. Hence, HCF (25, 36) = 1.
☛ Prime Numbers

What is the Relation Between LCM and HCF of 25, 36?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 25 and 36, i.e. HCF × LCM = 25 × 36.

What are the Methods to Find HCF of 25 and 36?

There are three commonly used methods to find the HCF of 25 and 36.

By Long Division
By Prime Factorization
By Euclidean Algorithm

If the HCF of 36 and 25 is 1, Find its LCM.

HCF(36, 25) × LCM(36, 25) = 36 × 25
Since the HCF of 36 and 25 = 1
⇒ 1 × LCM(36, 25) = 900
Therefore, LCM = 900
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