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

GCF of 30 and 50

GCF of 30 and 50 is the largest possible number that divides 30 and 50 exactly without any remainder. The factors of 30 and 50 are 1, 2, 3, 5, 6, 10, 15, 30 and 1, 2, 5, 10, 25, 50 respectively. There are 3 commonly used methods to find the GCF of 30 and 50 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 30 and 50
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 30 and 50?

Answer: GCF of 30 and 50 is 10.

Explanation:

The GCF of two non-zero integers, x(30) and y(50), is the greatest positive integer m(10) that divides both x(30) and y(50) without any remainder.

Methods to Find GCF of 30 and 50

Let's look at the different methods for finding the GCF of 30 and 50.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 30 and 50 by Prime Factorization

Prime factorization of 30 and 50 is (2 × 3 × 5) and (2 × 5 × 5) respectively. As visible, 30 and 50 have common prime factors. Hence, the GCF of 30 and 50 is 2 × 5 = 10.

GCF of 30 and 50 by Long Division

GCF of 30 and 50 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 50 (larger number) by 30 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (30) by the remainder (20).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (10) is the GCF of 30 and 50.

GCF of 30 and 50 by Listing Common Factors

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 50: 1, 2, 5, 10, 25, 50

There are 4 common factors of 30 and 50, that are 1, 2, 10, and 5. Therefore, the greatest common factor of 30 and 50 is 10.

☛ Also Check:

GCF of 30 and 50 Examples

Example 1: For two numbers, GCF = 10 and LCM = 150. If one number is 50, find the other number.

Solution:

Given: GCF (z, 50) = 10 and LCM (z, 50) = 150
∵ GCF × LCM = 50 × (z)
⇒ z = (GCF × LCM)/50
⇒ z = (10 × 150)/50
⇒ z = 30
Therefore, the other number is 30.
Example 2: Find the GCF of 30 and 50, if their LCM is 150.

Solution:

∵ LCM × GCF = 30 × 50
⇒ GCF(30, 50) = (30 × 50)/150 = 10
Therefore, the greatest common factor of 30 and 50 is 10.
Example 3: Find the greatest number that divides 30 and 50 exactly.

Solution:

The greatest number that divides 30 and 50 exactly is their greatest common factor, i.e. GCF of 30 and 50.
⇒ Factors of 30 and 50:
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 50 = 1, 2, 5, 10, 25, 50
Therefore, the GCF of 30 and 50 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 30 and 50

What is the GCF of 30 and 50?

The GCF of 30 and 50 is 10. To calculate the GCF of 30 and 50, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 50 = 1, 2, 5, 10, 25, 50) and choose the greatest factor that exactly divides both 30 and 50, i.e., 10.

How to Find the GCF of 30 and 50 by Prime Factorization?

To find the GCF of 30 and 50, we will find the prime factorization of the given numbers, i.e. 30 = 2 × 3 × 5; 50 = 2 × 5 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 30 and 50. Hence, GCF(30, 50) = 2 × 5 = 10
☛ What is a Prime Number?

If the GCF of 50 and 30 is 10, Find its LCM.

GCF(50, 30) × LCM(50, 30) = 50 × 30
Since the GCF of 50 and 30 = 10
⇒ 10 × LCM(50, 30) = 1500
Therefore, LCM = 150
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 30 and 50?

There are three commonly used methods to find the GCF of 30 and 50.

By Prime Factorization
By Listing Common Factors
By Long Division

How to Find the GCF of 30 and 50 by Long Division Method?

To find the GCF of 30, 50 using long division method, 50 is divided by 30. The corresponding divisor (10) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 30, 50?

The following equation can be used to express the relation between Least Common Multiple and GCF of 30 and 50, i.e. GCF × LCM = 30 × 50.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum