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GCF of 54 and 32

GCF of 54 and 32 is the largest possible number that divides 54 and 32 exactly without any remainder. The factors of 54 and 32 are 1, 2, 3, 6, 9, 18, 27, 54 and 1, 2, 4, 8, 16, 32 respectively. There are 3 commonly used methods to find the GCF of 54 and 32 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 54 and 32
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 54 and 32?

Answer: GCF of 54 and 32 is 2.

Explanation:

The GCF of two non-zero integers, x(54) and y(32), is the greatest positive integer m(2) that divides both x(54) and y(32) without any remainder.

Methods to Find GCF of 54 and 32

The methods to find the GCF of 54 and 32 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 54 and 32 by Listing Common Factors

Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Factors of 32: 1, 2, 4, 8, 16, 32

There are 2 common factors of 54 and 32, that are 1 and 2. Therefore, the greatest common factor of 54 and 32 is 2.

GCF of 54 and 32 by Long Division

GCF of 54 and 32 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 54 (larger number) by 32 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (32) by the remainder (22).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 54 and 32.

GCF of 54 and 32 by Prime Factorization

Prime factorization of 54 and 32 is (2 × 3 × 3 × 3) and (2 × 2 × 2 × 2 × 2) respectively. As visible, 54 and 32 have only one common prime factor i.e. 2. Hence, the GCF of 54 and 32 is 2.

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GCF of 54 and 32 Examples

Example 1: For two numbers, GCF = 2 and LCM = 864. If one number is 54, find the other number.

Solution:

Given: GCF (x, 54) = 2 and LCM (x, 54) = 864
∵ GCF × LCM = 54 × (x)
⇒ x = (GCF × LCM)/54
⇒ x = (2 × 864)/54
⇒ x = 32
Therefore, the other number is 32.
Example 2: Find the GCF of 54 and 32, if their LCM is 864.

Solution:

∵ LCM × GCF = 54 × 32
⇒ GCF(54, 32) = (54 × 32)/864 = 2
Therefore, the greatest common factor of 54 and 32 is 2.
Example 3: Find the greatest number that divides 54 and 32 exactly.

Solution:

The greatest number that divides 54 and 32 exactly is their greatest common factor, i.e. GCF of 54 and 32.
⇒ Factors of 54 and 32:
- Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54
- Factors of 32 = 1, 2, 4, 8, 16, 32
Therefore, the GCF of 54 and 32 is 2.

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FAQs on GCF of 54 and 32

What is the GCF of 54 and 32?

The GCF of 54 and 32 is 2. To calculate the GCF (Greatest Common Factor) of 54 and 32, we need to factor each number (factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54; factors of 32 = 1, 2, 4, 8, 16, 32) and choose the greatest factor that exactly divides both 54 and 32, i.e., 2.

If the GCF of 32 and 54 is 2, Find its LCM.

GCF(32, 54) × LCM(32, 54) = 32 × 54
Since the GCF of 32 and 54 = 2
⇒ 2 × LCM(32, 54) = 1728
Therefore, LCM = 864
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How to Find the GCF of 54 and 32 by Prime Factorization?

To find the GCF of 54 and 32, we will find the prime factorization of the given numbers, i.e. 54 = 2 × 3 × 3 × 3; 32 = 2 × 2 × 2 × 2 × 2.
⇒ Since 2 is the only common prime factor of 54 and 32. Hence, GCF (54, 32) = 2.
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What is the Relation Between LCM and GCF of 54, 32?

The following equation can be used to express the relation between LCM and GCF of 54 and 32, i.e. GCF × LCM = 54 × 32.

How to Find the GCF of 54 and 32 by Long Division Method?

To find the GCF of 54, 32 using long division method, 54 is divided by 32. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 54 and 32?

There are three commonly used methods to find the GCF of 54 and 32.

By Euclidean Algorithm
By Long Division
By Prime Factorization

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