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

HCF of 10, 20 and 30

HCF of 10, 20 and 30 is the largest possible number that divides 10, 20 and 30 exactly without any remainder. The factors of 10, 20 and 30 are (1, 2, 5, 10), (1, 2, 4, 5, 10, 20) and (1, 2, 3, 5, 6, 10, 15, 30) respectively. There are 3 commonly used methods to find the HCF of 10, 20 and 30 - prime factorization, Euclidean algorithm, and long division.

1.	HCF of 10, 20 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is HCF of 10, 20 and 30?

Answer: HCF of 10, 20 and 30 is 10.

Explanation:

The HCF of three non-zero integers, x(10), y(20) and z(30), is the highest positive integer m(10) that divides x(10), y(20) and z(30) without any remainder.

Methods to Find HCF of 10, 20 and 30

Let's look at the different methods for finding the HCF of 10, 20 and 30.

Prime Factorization Method
Listing Common Factors
Using Euclid's Algorithm

HCF of 10, 20 and 30 by Prime Factorization

Prime factorization of 10, 20 and 30 is (2 × 5), (2 × 2 × 5) and (2 × 3 × 5) respectively. As visible, 10, 20 and 30 have common prime factors. Hence, the HCF of 10, 20 and 30 is 2 × 5 = 10.

HCF of 10, 20 and 30 by Listing Common Factors

Factors of 10: 1, 2, 5, 10
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

There are 4 common factors of 10, 20 and 30, that are 1, 2, 10, and 5. Therefore, the highest common factor of 10, 20 and 30 is 10.

HCF of 10, 20 and 30 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.

HCF(10, 20, 30) = HCF(HCF(10, 20), 30)

HCF(20, 10) = HCF(10, 20 mod 10) = HCF(10, 0)
HCF(10, 0) = 10 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Steps for HCF(10, 30)

HCF(30, 10) = HCF(10, 30 mod 10) = HCF(10, 0)
HCF(10, 0) = 10 (∵ HCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of HCF of 10, 20 and 30 is 10.

☛ Also Check:

HCF of 10, 20 and 30 Examples

Example 1: Calculate the HCF of 10, 20, and 30 using LCM of the given numbers.

Solution:

Prime factorization of 10, 20 and 30 is given as,
- 10 = 2 × 5
- 20 = 2 × 2 × 5
- 30 = 2 × 3 × 5
LCM(10, 20) = 20, LCM(20, 30) = 60, LCM(30, 10) = 30, LCM(10, 20, 30) = 60
⇒ HCF(10, 20, 30) = [(10 × 20 × 30) × LCM(10, 20, 30)]/[LCM(10, 20) × LCM (20, 30) × LCM(30, 10)]
⇒ HCF(10, 20, 30) = (6000 × 60)/(20 × 60 × 30)
⇒ HCF(10, 20, 30) = 10.
Therefore, the HCF of 10, 20 and 30 is 10.
Example 2: Find the highest number that divides 10, 20, and 30 completely.

Solution:

The highest number that divides 10, 20, and 30 exactly is their highest common factor.
- Factors of 10 = 1, 2, 5, 10
- Factors of 20 = 1, 2, 4, 5, 10, 20
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
The HCF of 10, 20, and 30 is 10.
∴ The highest number that divides 10, 20, and 30 is 10.
Example 3: Verify the relation between the LCM and HCF of 10, 20 and 30.

Solution:

The relation between the LCM and HCF of 10, 20 and 30 is given as, HCF(10, 20, 30) = [(10 × 20 × 30) × LCM(10, 20, 30)]/[LCM(10, 20) × LCM (20, 30) × LCM(10, 30)]
⇒ Prime factorization of 10, 20 and 30:
- 10 = 2 × 5
- 20 = 2 × 2 × 5
- 30 = 2 × 3 × 5
∴ LCM of (10, 20), (20, 30), (10, 30), and (10, 20, 30) is 20, 60, 30, and 60 respectively.
Now, LHS = HCF(10, 20, 30) = 10.
And, RHS = [(10 × 20 × 30) × LCM(10, 20, 30)]/[LCM(10, 20) × LCM (20, 30) × LCM(10, 30)] = [(6000) × 60]/[20 × 60 × 30]
LHS = RHS = 10.
Hence verified.

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 10, 20 and 30

What is the HCF of 10, 20 and 30?

The HCF of 10, 20 and 30 is 10. To calculate the highest common factor of 10, 20 and 30, we need to factor each number (factors of 10 = 1, 2, 5, 10; factors of 20 = 1, 2, 4, 5, 10, 20; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the highest factor that exactly divides 10, 20 and 30, i.e., 10.

What is the Relation Between LCM and HCF of 10, 20 and 30?

The following equation can be used to express the relation between Least Common Multiple (LCM) and HCF of 10, 20 and 30, i.e. HCF(10, 20, 30) = [(10 × 20 × 30) × LCM(10, 20, 30)]/[LCM(10, 20) × LCM (20, 30) × LCM(10, 30)].
☛ Highest Common Factor Calculator

What are the Methods to Find HCF of 10, 20 and 30?

There are three commonly used methods to find the HCF of 10, 20 and 30.

By Euclidean Algorithm
By Prime Factorization
By Long Division

Which of the following is HCF of 10, 20 and 30? 10, 51, 44, 69, 50, 57

HCF of 10, 20, 30 will be the number that divides 10, 20, and 30 without leaving any remainder. The only number that satisfies the given condition is 10.

How to Find the HCF of 10, 20 and 30 by Prime Factorization?

To find the HCF of 10, 20 and 30, we will find the prime factorization of given numbers, i.e. 10 = 2 × 5; 20 = 2 × 2 × 5; 30 = 2 × 3 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 10, 20 and 30. Hence, HCF(10, 20, 30) = 2 × 5 = 10
☛ What is a Prime Number?

Download FREE Study Materials

HCF and LCM

Math worksheets and
visual curriculum