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GCF of 30 and 48

GCF of 30 and 48 is the largest possible number that divides 30 and 48 exactly without any remainder. The factors of 30 and 48 are 1, 2, 3, 5, 6, 10, 15, 30 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There are 3 commonly used methods to find the GCF of 30 and 48 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 30 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 30 and 48?

Answer: GCF of 30 and 48 is 6.

Explanation:

The GCF of two non-zero integers, x(30) and y(48), is the greatest positive integer m(6) that divides both x(30) and y(48) without any remainder.

Methods to Find GCF of 30 and 48

The methods to find the GCF of 30 and 48 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 30 and 48 by Long Division

GCF of 30 and 48 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 48 (larger number) by 30 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (30) by the remainder (18).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the GCF of 30 and 48.

GCF of 30 and 48 by Prime Factorization

Prime factorization of 30 and 48 is (2 × 3 × 5) and (2 × 2 × 2 × 2 × 3) respectively. As visible, 30 and 48 have common prime factors. Hence, the GCF of 30 and 48 is 2 × 3 = 6.

GCF of 30 and 48 by Listing Common Factors

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

There are 4 common factors of 30 and 48, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 30 and 48 is 6.

☛ Also Check:

GCF of 30 and 48 Examples

Example 1: For two numbers, GCF = 6 and LCM = 240. If one number is 30, find the other number.

Solution:

Given: GCF (x, 30) = 6 and LCM (x, 30) = 240
∵ GCF × LCM = 30 × (x)
⇒ x = (GCF × LCM)/30
⇒ x = (6 × 240)/30
⇒ x = 48
Therefore, the other number is 48.
Example 2: Find the greatest number that divides 30 and 48 exactly.

Solution:

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

Solution:

∵ LCM × GCF = 30 × 48
⇒ GCF(30, 48) = (30 × 48)/240 = 6
Therefore, the greatest common factor of 30 and 48 is 6.

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FAQs on GCF of 30 and 48

What is the GCF of 30 and 48?

The GCF of 30 and 48 is 6. To calculate the GCF of 30 and 48, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and choose the greatest factor that exactly divides both 30 and 48, i.e., 6.

How to Find the GCF of 30 and 48 by Prime Factorization?

To find the GCF of 30 and 48, we will find the prime factorization of the given numbers, i.e. 30 = 2 × 3 × 5; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 30 and 48. Hence, GCF(30, 48) = 2 × 3 = 6
☛ What is a Prime Number?

If the GCF of 48 and 30 is 6, Find its LCM.

GCF(48, 30) × LCM(48, 30) = 48 × 30
Since the GCF of 48 and 30 = 6
⇒ 6 × LCM(48, 30) = 1440
Therefore, LCM = 240
☛ GCF Calculator

What is the Relation Between LCM and GCF of 30, 48?

The following equation can be used to express the relation between Least Common Multiple and GCF of 30 and 48, i.e. GCF × LCM = 30 × 48.

What are the Methods to Find GCF of 30 and 48?

There are three commonly used methods to find the GCF of 30 and 48.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the GCF of 30 and 48 by Long Division Method?

To find the GCF of 30, 48 using long division method, 48 is divided by 30. The corresponding divisor (6) when remainder equals 0 is taken as GCF.

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