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

GCF of 72 and 36

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

1.	GCF of 72 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 72 and 36?

Answer: GCF of 72 and 36 is 36.

Explanation:

The GCF of two non-zero integers, x(72) and y(36), is the greatest positive integer m(36) that divides both x(72) and y(36) without any remainder.

Methods to Find GCF of 72 and 36

The methods to find the GCF of 72 and 36 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 72 and 36 by Long Division

GCF of 72 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 72 (larger number) by 36 (smaller number).
Step 2: Since the remainder = 0, the divisor (36) is the GCF of 72 and 36.

The corresponding divisor (36) is the GCF of 72 and 36.

GCF of 72 and 36 by Prime Factorization

Prime factorization of 72 and 36 is (2 × 2 × 2 × 3 × 3) and (2 × 2 × 3 × 3) respectively. As visible, 72 and 36 have common prime factors. Hence, the GCF of 72 and 36 is 2 × 2 × 3 × 3 = 36.

GCF of 72 and 36 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 = 72 and Y = 36

GCF(72, 36) = GCF(36, 72 mod 36) = GCF(36, 0)
GCF(36, 0) = 36 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 72 and 36 is 36.

☛ Also Check:

GCF of 72 and 36 Examples

Example 1: Find the GCF of 72 and 36, if their LCM is 72.

Solution:

∵ LCM × GCF = 72 × 36
⇒ GCF(72, 36) = (72 × 36)/72 = 36
Therefore, the greatest common factor of 72 and 36 is 36.
Example 2: The product of two numbers is 2592. If their GCF is 36, what is their LCM?

Solution:

Given: GCF = 36 and product of numbers = 2592
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2592/36
Therefore, the LCM is 72.
Example 3: For two numbers, GCF = 36 and LCM = 72. If one number is 72, find the other number.

Solution:

Given: GCF (x, 72) = 36 and LCM (x, 72) = 72
∵ GCF × LCM = 72 × (x)
⇒ x = (GCF × LCM)/72
⇒ x = (36 × 72)/72
⇒ x = 36
Therefore, the other number is 36.

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 36

What is the GCF of 72 and 36?

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

What is the Relation Between LCM and GCF of 72, 36?

The following equation can be used to express the relation between LCM and GCF of 72 and 36, i.e. GCF × LCM = 72 × 36.

What are the Methods to Find GCF of 72 and 36?

There are three commonly used methods to find the GCF of 72 and 36.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the GCF of 72 and 36 by Long Division Method?

To find the GCF of 72, 36 using long division method, 72 is divided by 36. The corresponding divisor (36) when remainder equals 0 is taken as GCF.

If the GCF of 36 and 72 is 36, Find its LCM.

GCF(36, 72) × LCM(36, 72) = 36 × 72
Since the GCF of 36 and 72 = 36
⇒ 36 × LCM(36, 72) = 2592
Therefore, LCM = 72
☛ GCF Calculator

How to Find the GCF of 72 and 36 by Prime Factorization?

To find the GCF of 72 and 36, we will find the prime factorization of the given numbers, i.e. 72 = 2 × 2 × 2 × 3 × 3; 36 = 2 × 2 × 3 × 3.
⇒ Since 2, 2, 3, 3 are common terms in the prime factorization of 72 and 36. Hence, GCF(72, 36) = 2 × 2 × 3 × 3 = 36
☛ What is a Prime Number?

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum