A day full of math games & activities. Find one near you.

HCF of 6 and 10

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

1.	HCF of 6 and 10
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 6 and 10?

Answer: HCF of 6 and 10 is 2.

Explanation:

The HCF of two non-zero integers, x(6) and y(10), is the highest positive integer m(2) that divides both x(6) and y(10) without any remainder.

Methods to Find HCF of 6 and 10

Let's look at the different methods for finding the HCF of 6 and 10.

Prime Factorization Method
Long Division Method
Listing Common Factors

HCF of 6 and 10 by Prime Factorization

Prime factorization of 6 and 10 is (2 × 3) and (2 × 5) respectively. As visible, 6 and 10 have only one common prime factor i.e. 2. Hence, the HCF of 6 and 10 is 2.

HCF of 6 and 10 by Long Division

HCF of 6 and 10 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 10 (larger number) by 6 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (6) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the HCF of 6 and 10.

HCF of 6 and 10 by Listing Common Factors

Factors of 6: 1, 2, 3, 6
Factors of 10: 1, 2, 5, 10

There are 2 common factors of 6 and 10, that are 1 and 2. Therefore, the highest common factor of 6 and 10 is 2.

☛ Also Check:

HCF of 6 and 10 Examples

Example 1: The product of two numbers is 60. If their HCF is 2, what is their LCM?

Solution:

Given: HCF = 2 and product of numbers = 60
∵ LCM × HCF = product of numbers
⇒ LCM = Product/HCF = 60/2
Therefore, the LCM is 30.
Example 2: Find the HCF of 6 and 10, if their LCM is 30.

Solution:

∵ LCM × HCF = 6 × 10
⇒ HCF(6, 10) = (6 × 10)/30 = 2
Therefore, the highest common factor of 6 and 10 is 2.
Example 3: For two numbers, HCF = 2 and LCM = 30. If one number is 10, find the other number.

Solution:

Given: HCF (z, 10) = 2 and LCM (z, 10) = 30
∵ HCF × LCM = 10 × (z)
⇒ z = (HCF × LCM)/10
⇒ z = (2 × 30)/10
⇒ z = 6
Therefore, the other number is 6.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on HCF of 6 and 10

What is the HCF of 6 and 10?

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

What are the Methods to Find HCF of 6 and 10?

There are three commonly used methods to find the HCF of 6 and 10.

By Long Division
By Euclidean Algorithm
By Prime Factorization

If the HCF of 10 and 6 is 2, Find its LCM.

HCF(10, 6) × LCM(10, 6) = 10 × 6
Since the HCF of 10 and 6 = 2
⇒ 2 × LCM(10, 6) = 60
Therefore, LCM = 30
☛ Highest Common Factor Calculator

What is the Relation Between LCM and HCF of 6, 10?

The following equation can be used to express the relation between LCM and HCF of 6 and 10, i.e. HCF × LCM = 6 × 10.

How to Find the HCF of 6 and 10 by Long Division Method?

To find the HCF of 6, 10 using long division method, 10 is divided by 6. The corresponding divisor (2) when remainder equals 0 is taken as HCF.

How to Find the HCF of 6 and 10 by Prime Factorization?

To find the HCF of 6 and 10, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 10 = 2 × 5.
⇒ Since 2 is the only common prime factor of 6 and 10. Hence, HCF (6, 10) = 2.
☛ What is a Prime Number?

Download FREE Study Materials

HCF and LCM

Math worksheets and
visual curriculum