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GCF of 18 and 48

GCF of 18 and 48 is the largest possible number that divides 18 and 48 exactly without any remainder. The factors of 18 and 48 are 1, 2, 3, 6, 9, 18 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There are 3 commonly used methods to find the GCF of 18 and 48 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 18 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 18 and 48?

Answer: GCF of 18 and 48 is 6.

Explanation:

The GCF of two non-zero integers, x(18) and y(48), is the greatest positive integer m(6) that divides both x(18) and y(48) without any remainder.

Methods to Find GCF of 18 and 48

The methods to find the GCF of 18 and 48 are explained below.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 18 and 48 by Long Division

GCF of 18 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 18 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (18) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the GCF of 18 and 48.

GCF of 18 and 48 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 = 48 and Y = 18

GCF(48, 18) = GCF(18, 48 mod 18) = GCF(18, 12)
GCF(18, 12) = GCF(12, 18 mod 12) = GCF(12, 6)
GCF(12, 6) = GCF(6, 12 mod 6) = GCF(6, 0)
GCF(6, 0) = 6 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 18 and 48 is 6.

GCF of 18 and 48 by Listing Common Factors

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

There are 4 common factors of 18 and 48, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 18 and 48 is 6.

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GCF of 18 and 48 Examples

Example 1: The product of two numbers is 864. If their GCF is 6, what is their LCM?

Solution:

Given: GCF = 6 and product of numbers = 864
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 864/6
Therefore, the LCM is 144.
Example 2: For two numbers, GCF = 6 and LCM = 144. If one number is 18, find the other number.

Solution:

Given: GCF (z, 18) = 6 and LCM (z, 18) = 144
∵ GCF × LCM = 18 × (z)
⇒ z = (GCF × LCM)/18
⇒ z = (6 × 144)/18
⇒ z = 48
Therefore, the other number is 48.
Example 3: Find the greatest number that divides 18 and 48 exactly.

Solution:

The greatest number that divides 18 and 48 exactly is their greatest common factor, i.e. GCF of 18 and 48.
⇒ Factors of 18 and 48:
- Factors of 18 = 1, 2, 3, 6, 9, 18
- Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Therefore, the GCF of 18 and 48 is 6.

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FAQs on GCF of 18 and 48

What is the GCF of 18 and 48?

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

How to Find the GCF of 18 and 48 by Long Division Method?

To find the GCF of 18, 48 using long division method, 48 is divided by 18. The corresponding divisor (6) when remainder equals 0 is taken as GCF.

If the GCF of 48 and 18 is 6, Find its LCM.

GCF(48, 18) × LCM(48, 18) = 48 × 18
Since the GCF of 48 and 18 = 6
⇒ 6 × LCM(48, 18) = 864
Therefore, LCM = 144
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What are the Methods to Find GCF of 18 and 48?

There are three commonly used methods to find the GCF of 18 and 48.

By Euclidean Algorithm
By Long Division
By Prime Factorization

What is the Relation Between LCM and GCF of 18, 48?

The following equation can be used to express the relation between Least Common Multiple and GCF of 18 and 48, i.e. GCF × LCM = 18 × 48.

How to Find the GCF of 18 and 48 by Prime Factorization?

To find the GCF of 18 and 48, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 18 and 48. Hence, GCF(18, 48) = 2 × 3 = 6
☛ What are Prime Numbers?

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