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

GCF of 60 and 72

GCF of 60 and 72 is the largest possible number that divides 60 and 72 exactly without any remainder. The factors of 60 and 72 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 respectively. There are 3 commonly used methods to find the GCF of 60 and 72 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 60 and 72
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 60 and 72?

Answer: GCF of 60 and 72 is 12.

Explanation:

The GCF of two non-zero integers, x(60) and y(72), is the greatest positive integer m(12) that divides both x(60) and y(72) without any remainder.

Methods to Find GCF of 60 and 72

Let's look at the different methods for finding the GCF of 60 and 72.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 60 and 72 by Long Division

GCF of 60 and 72 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 72 (larger number) by 60 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (60) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (12) is the GCF of 60 and 72.

GCF of 60 and 72 by Prime Factorization

Prime factorization of 60 and 72 is (2 × 2 × 3 × 5) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 60 and 72 have common prime factors. Hence, the GCF of 60 and 72 is 2 × 2 × 3 = 12.

GCF of 60 and 72 by Listing Common Factors

Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

There are 6 common factors of 60 and 72, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 60 and 72 is 12.

☛ Also Check:

GCF of 60 and 72 Examples

Example 1: For two numbers, GCF = 12 and LCM = 360. If one number is 60, find the other number.

Solution:

Given: GCF (z, 60) = 12 and LCM (z, 60) = 360
∵ GCF × LCM = 60 × (z)
⇒ z = (GCF × LCM)/60
⇒ z = (12 × 360)/60
⇒ z = 72
Therefore, the other number is 72.
Example 2: Find the greatest number that divides 60 and 72 exactly.

Solution:

The greatest number that divides 60 and 72 exactly is their greatest common factor, i.e. GCF of 60 and 72.
⇒ Factors of 60 and 72:
- Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Therefore, the GCF of 60 and 72 is 12.
Example 3: The product of two numbers is 4320. If their GCF is 12, what is their LCM?

Solution:

Given: GCF = 12 and product of numbers = 4320
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 4320/12
Therefore, the LCM is 360.

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 60 and 72

What is the GCF of 60 and 72?

The GCF of 60 and 72 is 12. To calculate the GCF of 60 and 72, we need to factor each number (factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the greatest factor that exactly divides both 60 and 72, i.e., 12.

What are the Methods to Find GCF of 60 and 72?

There are three commonly used methods to find the GCF of 60 and 72.

By Long Division
By Prime Factorization
By Euclidean Algorithm

If the GCF of 72 and 60 is 12, Find its LCM.

GCF(72, 60) × LCM(72, 60) = 72 × 60
Since the GCF of 72 and 60 = 12
⇒ 12 × LCM(72, 60) = 4320
Therefore, LCM = 360
☛ Greatest Common Factor Calculator

How to Find the GCF of 60 and 72 by Long Division Method?

To find the GCF of 60, 72 using long division method, 72 is divided by 60. The corresponding divisor (12) when remainder equals 0 is taken as GCF.

How to Find the GCF of 60 and 72 by Prime Factorization?

To find the GCF of 60 and 72, we will find the prime factorization of the given numbers, i.e. 60 = 2 × 2 × 3 × 5; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 60 and 72. Hence, GCF(60, 72) = 2 × 2 × 3 = 12
☛ What is a Prime Number?

What is the Relation Between LCM and GCF of 60, 72?

The following equation can be used to express the relation between LCM and GCF of 60 and 72, i.e. GCF × LCM = 60 × 72.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum