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

GCF of 72 and 120

GCF of 72 and 120 is the largest possible number that divides 72 and 120 exactly without any remainder. The factors of 72 and 120 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 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 72 and 120 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 72 and 120
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 72 and 120?

Answer: GCF of 72 and 120 is 24.

Explanation:

The GCF of two non-zero integers, x(72) and y(120), is the greatest positive integer m(24) that divides both x(72) and y(120) without any remainder.

Methods to Find GCF of 72 and 120

Let's look at the different methods for finding the GCF of 72 and 120.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 72 and 120 by Long Division

GCF of 72 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 72 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (72) by the remainder (48).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (24) is the GCF of 72 and 120.

GCF of 72 and 120 by Listing Common Factors

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
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 72 and 120, that are 1, 2, 3, 4, 6, 8, 12, and 24. Therefore, the greatest common factor of 72 and 120 is 24.

GCF of 72 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 = 72

GCF(120, 72) = GCF(72, 120 mod 72) = GCF(72, 48)
GCF(72, 48) = GCF(48, 72 mod 48) = GCF(48, 24)
GCF(48, 24) = GCF(24, 48 mod 24) = GCF(24, 0)
GCF(24, 0) = 24 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 72 and 120 is 24.

☛ Also Check:

GCF of 72 and 120 Examples

Example 1: Find the GCF of 72 and 120, if their LCM is 360.

Solution:

∵ LCM × GCF = 72 × 120
⇒ GCF(72, 120) = (72 × 120)/360 = 24
Therefore, the greatest common factor of 72 and 120 is 24.
Example 2: Find the greatest number that divides 72 and 120 exactly.

Solution:

The greatest number that divides 72 and 120 exactly is their greatest common factor, i.e. GCF of 72 and 120.
⇒ Factors of 72 and 120:
- Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Therefore, the GCF of 72 and 120 is 24.
Example 3: For two numbers, GCF = 24 and LCM = 360. If one number is 120, find the other number.

Solution:

Given: GCF (x, 120) = 24 and LCM (x, 120) = 360
∵ GCF × LCM = 120 × (x)
⇒ x = (GCF × LCM)/120
⇒ x = (24 × 360)/120
⇒ x = 72
Therefore, the other number is 72.

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 72 and 120

What is the GCF of 72 and 120?

The GCF of 72 and 120 is 24. To calculate the greatest common factor of 72 and 120, we need to factor each number (factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72; 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 72 and 120, i.e., 24.

What are the Methods to Find GCF of 72 and 120?

There are three commonly used methods to find the GCF of 72 and 120.

By Prime Factorization
By Long Division
By Euclidean Algorithm

What is the Relation Between LCM and GCF of 72, 120?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 72 and 120, i.e. GCF × LCM = 72 × 120.

How to Find the GCF of 72 and 120 by Long Division Method?

To find the GCF of 72, 120 using long division method, 120 is divided by 72. The corresponding divisor (24) when remainder equals 0 is taken as GCF.

How to Find the GCF of 72 and 120 by Prime Factorization?

To find the GCF of 72 and 120, we will find the prime factorization of the given numbers, i.e. 72 = 2 × 2 × 2 × 3 × 3; 120 = 2 × 2 × 2 × 3 × 5.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 72 and 120. Hence, GCF(72, 120) = 2 × 2 × 2 × 3 = 24
☛ What is a Prime Number?

If the GCF of 120 and 72 is 24, Find its LCM.

GCF(120, 72) × LCM(120, 72) = 120 × 72
Since the GCF of 120 and 72 = 24
⇒ 24 × LCM(120, 72) = 8640
Therefore, LCM = 360
☛ Greatest Common Factor Calculator

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum