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GCF of 48 and 120

GCF of 48 and 120 is the largest possible number that divides 48 and 120 exactly without any remainder. The factors of 48 and 120 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 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 48 and 120 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 48 and 120
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 48 and 120?

Answer: GCF of 48 and 120 is 24.

Explanation:

The GCF of two non-zero integers, x(48) and y(120), is the greatest positive integer m(24) that divides both x(48) and y(120) without any remainder.

Methods to Find GCF of 48 and 120

The methods to find the GCF of 48 and 120 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 48 and 120 by Long Division

GCF of 48 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 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 120.

GCF of 48 and 120 by Prime Factorization

Prime factorization of 48 and 120 is (2 × 2 × 2 × 2 × 3) and (2 × 2 × 2 × 3 × 5) respectively. As visible, 48 and 120 have common prime factors. Hence, the GCF of 48 and 120 is 2 × 2 × 2 × 3 = 24.

GCF of 48 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 = 48

GCF(120, 48) = GCF(48, 120 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 120 is 24.

☛ Also Check:

GCF of 48 and 120 Examples

Example 1: For two numbers, GCF = 24 and LCM = 240. If one number is 48, find the other number.

Solution:

Given: GCF (y, 48) = 24 and LCM (y, 48) = 240
∵ GCF × LCM = 48 × (y)
⇒ y = (GCF × LCM)/48
⇒ y = (24 × 240)/48
⇒ y = 120
Therefore, the other number is 120.
Example 2: Find the greatest number that divides 48 and 120 exactly.

Solution:

The greatest number that divides 48 and 120 exactly is their greatest common factor, i.e. GCF of 48 and 120.
⇒ Factors of 48 and 120:
- Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Therefore, the GCF of 48 and 120 is 24.
Example 3: Find the GCF of 48 and 120, if their LCM is 240.

Solution:

∵ LCM × GCF = 48 × 120
⇒ GCF(48, 120) = (48 × 120)/240 = 24
Therefore, the greatest common factor of 48 and 120 is 24.

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FAQs on GCF of 48 and 120

What is the GCF of 48 and 120?

The GCF of 48 and 120 is 24. To calculate the GCF of 48 and 120, we need to factor each number (factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48; 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 48 and 120, i.e., 24.

What is the Relation Between LCM and GCF of 48, 120?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 48 and 120, i.e. GCF × LCM = 48 × 120.

How to Find the GCF of 48 and 120 by Long Division Method?

To find the GCF of 48, 120 using long division method, 120 is divided by 48. The corresponding divisor (24) when remainder equals 0 is taken as GCF.

How to Find the GCF of 48 and 120 by Prime Factorization?

To find the GCF of 48 and 120, we will find the prime factorization of the given numbers, i.e. 48 = 2 × 2 × 2 × 2 × 3; 120 = 2 × 2 × 2 × 3 × 5.
⇒ Since 2, 2, 2, 3 are common terms in the prime factorization of 48 and 120. Hence, GCF(48, 120) = 2 × 2 × 2 × 3 = 24
☛ What is a Prime Number?

If the GCF of 120 and 48 is 24, Find its LCM.

GCF(120, 48) × LCM(120, 48) = 120 × 48
Since the GCF of 120 and 48 = 24
⇒ 24 × LCM(120, 48) = 5760
Therefore, LCM = 240
☛ GCF Calculator

What are the Methods to Find GCF of 48 and 120?

There are three commonly used methods to find the GCF of 48 and 120.

By Long Division
By Listing Common Factors
By Prime Factorization

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