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

GCF of 10 and 30

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

1.	GCF of 10 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 10 and 30?

Answer: GCF of 10 and 30 is 10.

Explanation:

The GCF of two non-zero integers, x(10) and y(30), is the greatest positive integer m(10) that divides both x(10) and y(30) without any remainder.

Methods to Find GCF of 10 and 30

The methods to find the GCF of 10 and 30 are explained below.

Prime Factorization Method
Using Euclid's Algorithm
Long Division Method

GCF of 10 and 30 by Prime Factorization

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

GCF of 10 and 30 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 30 and Y = 10

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

Therefore, the value of GCF of 10 and 30 is 10.

GCF of 10 and 30 by Long Division

GCF of 10 and 30 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 30 (larger number) by 10 (smaller number).
Step 2: Since the remainder = 0, the divisor (10) is the GCF of 10 and 30.

The corresponding divisor (10) is the GCF of 10 and 30.

☛ Also Check:

GCF of 10 and 30 Examples

Example 1: Find the GCF of 10 and 30, if their LCM is 30.

Solution:

∵ LCM × GCF = 10 × 30
⇒ GCF(10, 30) = (10 × 30)/30 = 10
Therefore, the greatest common factor of 10 and 30 is 10.
Example 2: The product of two numbers is 300. If their GCF is 10, what is their LCM?

Solution:

Given: GCF = 10 and product of numbers = 300
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 300/10
Therefore, the LCM is 30.
Example 3: Find the greatest number that divides 10 and 30 exactly.

Solution:

The greatest number that divides 10 and 30 exactly is their greatest common factor, i.e. GCF of 10 and 30.
⇒ Factors of 10 and 30:
- Factors of 10 = 1, 2, 5, 10
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Therefore, the GCF of 10 and 30 is 10.

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 GCF of 10 and 30

What is the GCF of 10 and 30?

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

How to Find the GCF of 10 and 30 by Long Division Method?

To find the GCF of 10, 30 using long division method, 30 is divided by 10. The corresponding divisor (10) when remainder equals 0 is taken as GCF.

If the GCF of 30 and 10 is 10, Find its LCM.

GCF(30, 10) × LCM(30, 10) = 30 × 10
Since the GCF of 30 and 10 = 10
⇒ 10 × LCM(30, 10) = 300
Therefore, LCM = 30
☛ Greatest Common Factor Calculator

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

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 10 and 30, i.e. GCF × LCM = 10 × 30.

What are the Methods to Find GCF of 10 and 30?

There are three commonly used methods to find the GCF of 10 and 30.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 10 and 30 by Prime Factorization?

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

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum