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

GCF of 80 and 120

GCF of 80 and 120 is the largest possible number that divides 80 and 120 exactly without any remainder. The factors of 80 and 120 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 respectively. There are 3 commonly used methods to find the GCF of 80 and 120 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 80 and 120
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 80 and 120?

Answer: GCF of 80 and 120 is 40.

Explanation:

The GCF of two non-zero integers, x(80) and y(120), is the greatest positive integer m(40) that divides both x(80) and y(120) without any remainder.

Methods to Find GCF of 80 and 120

The methods to find the GCF of 80 and 120 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 80 and 120 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 = 120 and Y = 80

GCF(120, 80) = GCF(80, 120 mod 80) = GCF(80, 40)
GCF(80, 40) = GCF(40, 80 mod 40) = GCF(40, 0)
GCF(40, 0) = 40 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 80 and 120 is 40.

GCF of 80 and 120 by Long Division

GCF of 80 and 120 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 120 (larger number) by 80 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (80) by the remainder (40).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (40) is the GCF of 80 and 120.

GCF of 80 and 120 by Listing Common Factors

Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

There are 8 common factors of 80 and 120, that are 1, 2, 4, 5, 8, 40, 10, and 20. Therefore, the greatest common factor of 80 and 120 is 40.

☛ Also Check:

GCF of 80 and 120 Examples

Example 1: Find the greatest number that divides 80 and 120 exactly.

Solution:

The greatest number that divides 80 and 120 exactly is their greatest common factor, i.e. GCF of 80 and 120.
⇒ Factors of 80 and 120:
- Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
- Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Therefore, the GCF of 80 and 120 is 40.
Example 2: For two numbers, GCF = 40 and LCM = 240. If one number is 80, find the other number.

Solution:

Given: GCF (z, 80) = 40 and LCM (z, 80) = 240
∵ GCF × LCM = 80 × (z)
⇒ z = (GCF × LCM)/80
⇒ z = (40 × 240)/80
⇒ z = 120
Therefore, the other number is 120.
Example 3: Find the GCF of 80 and 120, if their LCM is 240.

Solution:

∵ LCM × GCF = 80 × 120
⇒ GCF(80, 120) = (80 × 120)/240 = 40
Therefore, the greatest common factor of 80 and 120 is 40.

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 80 and 120

What is the GCF of 80 and 120?

The GCF of 80 and 120 is 40. To calculate the GCF of 80 and 120, we need to factor each number (factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80; factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120) and choose the greatest factor that exactly divides both 80 and 120, i.e., 40.

How to Find the GCF of 80 and 120 by Prime Factorization?

To find the GCF of 80 and 120, we will find the prime factorization of the given numbers, i.e. 80 = 2 × 2 × 2 × 2 × 5; 120 = 2 × 2 × 2 × 3 × 5.
⇒ Since 2, 2, 2, 5 are common terms in the prime factorization of 80 and 120. Hence, GCF(80, 120) = 2 × 2 × 2 × 5 = 40
☛ What are Prime Numbers?

What are the Methods to Find GCF of 80 and 120?

There are three commonly used methods to find the GCF of 80 and 120.

By Long Division
By Prime Factorization
By Listing Common Factors

What is the Relation Between LCM and GCF of 80, 120?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 80 and 120, i.e. GCF × LCM = 80 × 120.

How to Find the GCF of 80 and 120 by Long Division Method?

To find the GCF of 80, 120 using long division method, 120 is divided by 80. The corresponding divisor (40) when remainder equals 0 is taken as GCF.

If the GCF of 120 and 80 is 40, Find its LCM.

GCF(120, 80) × LCM(120, 80) = 120 × 80
Since the GCF of 120 and 80 = 40
⇒ 40 × LCM(120, 80) = 9600
Therefore, LCM = 240
☛ GCF Calculator

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum