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GCF of 6 and 48

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

1.	GCF of 6 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 6 and 48?

Answer: GCF of 6 and 48 is 6.

Explanation:

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

Methods to Find GCF of 6 and 48

The methods to find the GCF of 6 and 48 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 6 and 48 by Prime Factorization

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

GCF of 6 and 48 by Listing Common Factors

Factors of 6: 1, 2, 3, 6
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

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

GCF of 6 and 48 by Long Division

GCF of 6 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 6 (smaller number).
Step 2: Since the remainder = 0, the divisor (6) is the GCF of 6 and 48.

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

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GCF of 6 and 48 Examples

Example 1: Find the GCF of 6 and 48, if their LCM is 48.

Solution:

∵ LCM × GCF = 6 × 48
⇒ GCF(6, 48) = (6 × 48)/48 = 6
Therefore, the greatest common factor of 6 and 48 is 6.
Example 2: Find the greatest number that divides 6 and 48 exactly.

Solution:

The greatest number that divides 6 and 48 exactly is their greatest common factor, i.e. GCF of 6 and 48.
⇒ Factors of 6 and 48:
- Factors of 6 = 1, 2, 3, 6
- Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Therefore, the GCF of 6 and 48 is 6.
Example 3: For two numbers, GCF = 6 and LCM = 48. If one number is 48, find the other number.

Solution:

Given: GCF (z, 48) = 6 and LCM (z, 48) = 48
∵ GCF × LCM = 48 × (z)
⇒ z = (GCF × LCM)/48
⇒ z = (6 × 48)/48
⇒ z = 6
Therefore, the other number is 6.

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FAQs on GCF of 6 and 48

What is the GCF of 6 and 48?

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

How to Find the GCF of 6 and 48 by Long Division Method?

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

What is the Relation Between LCM and GCF of 6, 48?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 6 and 48, i.e. GCF × LCM = 6 × 48.

What are the Methods to Find GCF of 6 and 48?

There are three commonly used methods to find the GCF of 6 and 48.

By Prime Factorization
By Long Division
By Listing Common Factors

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

GCF(48, 6) × LCM(48, 6) = 48 × 6
Since the GCF of 48 and 6 = 6
⇒ 6 × LCM(48, 6) = 288
Therefore, LCM = 48
☛ Greatest Common Factor Calculator

How to Find the GCF of 6 and 48 by Prime Factorization?

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

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