HCF of 6 and 20

HCF of 6 and 20 is the largest possible number that divides 6 and 20 exactly without any remainder. The factors of 6 and 20 are 1, 2, 3, 6 and 1, 2, 4, 5, 10, 20 respectively. There are 3 commonly used methods to find the HCF of 6 and 20 - long division, prime factorization, and Euclidean algorithm.

Answer: HCF of 6 and 20 is 2.

Explanation:

The HCF of two non-zero integers, x(6) and y(20), is the highest positive integer m(2) that divides both x(6) and y(20) without any remainder.

Let's look at the different methods for finding the HCF of 6 and 20.

• Prime Factorization Method
• Using Euclid's Algorithm
• Long Division Method

HCF of 6 and 20 by Prime Factorization

Prime factorization of 6 and 20 is (2 × 3) and (2 × 2 × 5) respectively. As visible, 6 and 20 have only one common prime factor i.e. 2. Hence, the HCF of 6 and 20 is 2.

HCF of 6 and 20 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 = 20 and Y = 6

• HCF(20, 6) = HCF(6, 20 mod 6) = HCF(6, 2)
• HCF(6, 2) = HCF(2, 6 mod 2) = HCF(2, 0)
• HCF(2, 0) = 2 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 6 and 20 is 2.

HCF of 6 and 20 by Long Division

HCF of 6 and 20 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

• Step 1: Divide 20 (larger number) by 6 (smaller number).
• Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (6) by the remainder (2).
• Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the HCF of 6 and 20.

☛ Also Check:

• HCF of 32 and 40 = 8
• HCF of 12, 16 and 24 = 4
• HCF of 186 and 403 = 31
• HCF of 324 and 144 = 36
• HCF of 72, 108 and 180 = 36
• HCF of 20 and 35 = 5
• HCF of 36 and 144 = 36

FAQs on HCF of 6 and 20

What is the HCF of 6 and 20?

The HCF of 6 and 20 is 2. To calculate the Highest common factor of 6 and 20, we need to factor each number (factors of 6 = 1, 2, 3, 6; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the highest factor that exactly divides both 6 and 20, i.e., 2.

What is the Relation Between LCM and HCF of 6, 20?

The following equation can be used to express the relation between LCM and HCF of 6 and 20, i.e. HCF × LCM = 6 × 20.

If the HCF of 20 and 6 is 2, Find its LCM.

HCF(20, 6) × LCM(20, 6) = 20 × 6
Since the HCF of 20 and 6 = 2
⇒ 2 × LCM(20, 6) = 120
Therefore, LCM = 60
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 6 and 20?

There are three commonly used methods to find the HCF of 6 and 20.

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

How to Find the HCF of 6 and 20 by Prime Factorization?

To find the HCF of 6 and 20, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 20 = 2 × 2 × 5.
⇒ Since 2 is the only common prime factor of 6 and 20. Hence, HCF (6, 20) = 2.
☛ What are Prime Numbers?

How to Find the HCF of 6 and 20 by Long Division Method?

To find the HCF of 6, 20 using long division method, 20 is divided by 6. The corresponding divisor (2) when remainder equals 0 is taken as HCF.