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GCF of 63 and 54

GCF of 63 and 54 is the largest possible number that divides 63 and 54 exactly without any remainder. The factors of 63 and 54 are 1, 3, 7, 9, 21, 63 and 1, 2, 3, 6, 9, 18, 27, 54 respectively. There are 3 commonly used methods to find the GCF of 63 and 54 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 63 and 54
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 63 and 54?

Answer: GCF of 63 and 54 is 9.

Explanation:

The GCF of two non-zero integers, x(63) and y(54), is the greatest positive integer m(9) that divides both x(63) and y(54) without any remainder.

Methods to Find GCF of 63 and 54

Let's look at the different methods for finding the GCF of 63 and 54.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

GCF of 63 and 54 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 = 63 and Y = 54

GCF(63, 54) = GCF(54, 63 mod 54) = GCF(54, 9)
GCF(54, 9) = GCF(9, 54 mod 9) = GCF(9, 0)
GCF(9, 0) = 9 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 63 and 54 is 9.

GCF of 63 and 54 by Listing Common Factors

Factors of 63: 1, 3, 7, 9, 21, 63
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

There are 3 common factors of 63 and 54, that are 1, 3, and 9. Therefore, the greatest common factor of 63 and 54 is 9.

GCF of 63 and 54 by Long Division

GCF of 63 and 54 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 63 (larger number) by 54 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (54) by the remainder (9).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (9) is the GCF of 63 and 54.

☛ Also Check:

GCF of 63 and 54 Examples

Example 1: Find the greatest number that divides 63 and 54 exactly.

Solution:

The greatest number that divides 63 and 54 exactly is their greatest common factor, i.e. GCF of 63 and 54.
⇒ Factors of 63 and 54:
- Factors of 63 = 1, 3, 7, 9, 21, 63
- Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54
Therefore, the GCF of 63 and 54 is 9.
Example 2: For two numbers, GCF = 9 and LCM = 378. If one number is 63, find the other number.

Solution:

Given: GCF (y, 63) = 9 and LCM (y, 63) = 378
∵ GCF × LCM = 63 × (y)
⇒ y = (GCF × LCM)/63
⇒ y = (9 × 378)/63
⇒ y = 54
Therefore, the other number is 54.
Example 3: Find the GCF of 63 and 54, if their LCM is 378.

Solution:

∵ LCM × GCF = 63 × 54
⇒ GCF(63, 54) = (63 × 54)/378 = 9
Therefore, the greatest common factor of 63 and 54 is 9.

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FAQs on GCF of 63 and 54

What is the GCF of 63 and 54?

The GCF of 63 and 54 is 9. To calculate the greatest common factor of 63 and 54, we need to factor each number (factors of 63 = 1, 3, 7, 9, 21, 63; factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54) and choose the greatest factor that exactly divides both 63 and 54, i.e., 9.

How to Find the GCF of 63 and 54 by Prime Factorization?

To find the GCF of 63 and 54, we will find the prime factorization of the given numbers, i.e. 63 = 3 × 3 × 7; 54 = 2 × 3 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 63 and 54. Hence, GCF(63, 54) = 3 × 3 = 9
☛ What is a Prime Number?

If the GCF of 54 and 63 is 9, Find its LCM.

GCF(54, 63) × LCM(54, 63) = 54 × 63
Since the GCF of 54 and 63 = 9
⇒ 9 × LCM(54, 63) = 3402
Therefore, LCM = 378
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 63 and 54?

There are three commonly used methods to find the GCF of 63 and 54.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the GCF of 63 and 54 by Long Division Method?

To find the GCF of 63, 54 using long division method, 63 is divided by 54. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 63, 54?

The following equation can be used to express the relation between LCM and GCF of 63 and 54, i.e. GCF × LCM = 63 × 54.

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