HCF of 20 and 25

HCF of 20 and 25 is the largest possible number that divides 20 and 25 exactly without any remainder. The factors of 20 and 25 are 1, 2, 4, 5, 10, 20 and 1, 5, 25 respectively. There are 3 commonly used methods to find the HCF of 20 and 25 - Euclidean algorithm, prime factorization, and long division.

Answer: HCF of 20 and 25 is 5.

Explanation:

The HCF of two non-zero integers, x(20) and y(25), is the highest positive integer m(5) that divides both x(20) and y(25) without any remainder.

Let's look at the different methods for finding the HCF of 20 and 25.

• Using Euclid's Algorithm
• Listing Common Factors
• Long Division Method

HCF of 20 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 = 20

• HCF(25, 20) = HCF(20, 25 mod 20) = HCF(20, 5)
• HCF(20, 5) = HCF(5, 20 mod 5) = HCF(5, 0)
• HCF(5, 0) = 5 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 20 and 25 is 5.

HCF of 20 and 25 by Listing Common Factors

• Factors of 20: 1, 2, 4, 5, 10, 20
• Factors of 25: 1, 5, 25

There are 2 common factors of 20 and 25, that are 1 and 5. Therefore, the highest common factor of 20 and 25 is 5.

HCF of 20 and 25 by Long Division

HCF of 20 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 20 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (5).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the HCF of 20 and 25.

☛ Also Check:

• HCF of 12 and 24 = 12
• HCF of 210 and 55 = 5
• HCF of 4052 and 420 = 4
• HCF of 1651 and 2032 = 127
• HCF of 70, 105 and 175 = 35
• HCF of 12, 45 and 75 = 3
• HCF of 4 and 8 = 4

FAQs on HCF of 20 and 25

What is the HCF of 20 and 25?

The HCF of 20 and 25 is 5. To calculate the HCF (Highest Common Factor) of 20 and 25, we need to factor each number (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 25 = 1, 5, 25) and choose the highest factor that exactly divides both 20 and 25, i.e., 5.

If the HCF of 25 and 20 is 5, Find its LCM.

HCF(25, 20) × LCM(25, 20) = 25 × 20
Since the HCF of 25 and 20 = 5
⇒ 5 × LCM(25, 20) = 500
Therefore, LCM = 100
☛ Highest Common Factor Calculator

How to Find the HCF of 20 and 25 by Long Division Method?

To find the HCF of 20, 25 using long division method, 25 is divided by 20. The corresponding divisor (5) when remainder equals 0 is taken as HCF.

How to Find the HCF of 20 and 25 by Prime Factorization?

To find the HCF of 20 and 25, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 25 = 5 × 5.
⇒ Since 5 is the only common prime factor of 20 and 25. Hence, HCF (20, 25) = 5.
☛ Prime Numbers

What are the Methods to Find HCF of 20 and 25?

There are three commonly used methods to find the HCF of 20 and 25.

• By Listing Common Factors
• By Long Division
• By Prime Factorization

What is the Relation Between LCM and HCF of 20, 25?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 20 and 25, i.e. HCF × LCM = 20 × 25.