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

GCF of 48 and 72

GCF of 48 and 72 is the largest possible number that divides 48 and 72 exactly without any remainder. The factors of 48 and 72 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 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 48 and 72 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 48 and 72
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 48 and 72?

Answer: GCF of 48 and 72 is 24.

Explanation:

The GCF of two non-zero integers, x(48) and y(72), is the greatest positive integer m(24) that divides both x(48) and y(72) without any remainder.

Methods to Find GCF of 48 and 72

The methods to find the GCF of 48 and 72 are explained below.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

GCF of 48 and 72 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 = 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 48 and 72 is 24.

GCF of 48 and 72 by Prime Factorization

Prime factorization of 48 and 72 is (2 × 2 × 2 × 2 × 3) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 48 and 72 have common prime factors. Hence, the GCF of 48 and 72 is 2 × 2 × 2 × 3 = 24.

GCF of 48 and 72 by Long Division

GCF of 48 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 48 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (48) by the remainder (24).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (24) is the GCF of 48 and 72.

☛ Also Check:

GCF of 48 and 72 Examples

Example 1: Find the GCF of 48 and 72, if their LCM is 144.

Solution:

∵ LCM × GCF = 48 × 72
⇒ GCF(48, 72) = (48 × 72)/144 = 24
Therefore, the greatest common factor of 48 and 72 is 24.
Example 2: For two numbers, GCF = 24 and LCM = 144. If one number is 72, find the other number.

Solution:

Given: GCF (y, 72) = 24 and LCM (y, 72) = 144
∵ GCF × LCM = 72 × (y)
⇒ y = (GCF × LCM)/72
⇒ y = (24 × 144)/72
⇒ y = 48
Therefore, the other number is 48.
Example 3: The product of two numbers is 3456. If their GCF is 24, what is their LCM?

Solution:

Given: GCF = 24 and product of numbers = 3456
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 3456/24
Therefore, the LCM is 144.

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 48 and 72

What is the GCF of 48 and 72?

The GCF of 48 and 72 is 24. To calculate the greatest common factor of 48 and 72, we need to factor each number (factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the greatest factor that exactly divides both 48 and 72, i.e., 24.

How to Find the GCF of 48 and 72 by Prime Factorization?

To find the GCF of 48 and 72, we will find the prime factorization of the given numbers, i.e. 48 = 2 × 2 × 2 × 2 × 3; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 48 and 72. Hence, GCF(48, 72) = 2 × 2 × 2 × 3 = 24
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 48, 72?

The following equation can be used to express the relation between LCM and GCF of 48 and 72, i.e. GCF × LCM = 48 × 72.

How to Find the GCF of 48 and 72 by Long Division Method?

To find the GCF of 48, 72 using long division method, 72 is divided by 48. The corresponding divisor (24) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 48 and 72?

There are three commonly used methods to find the GCF of 48 and 72.

By Prime Factorization
By Listing Common Factors
By Long Division

If the GCF of 72 and 48 is 24, Find its LCM.

GCF(72, 48) × LCM(72, 48) = 72 × 48
Since the GCF of 72 and 48 = 24
⇒ 24 × LCM(72, 48) = 3456
Therefore, LCM = 144
☛ Greatest Common Factor Calculator

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum