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GCF of 63 and 81

GCF of 63 and 81 is the largest possible number that divides 63 and 81 exactly without any remainder. The factors of 63 and 81 are 1, 3, 7, 9, 21, 63 and 1, 3, 9, 27, 81 respectively. There are 3 commonly used methods to find the GCF of 63 and 81 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 63 and 81
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 63 and 81?

Answer: GCF of 63 and 81 is 9.

Explanation:

The GCF of two non-zero integers, x(63) and y(81), is the greatest positive integer m(9) that divides both x(63) and y(81) without any remainder.

Methods to Find GCF of 63 and 81

The methods to find the GCF of 63 and 81 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 63 and 81 by Prime Factorization

Prime factorization of 63 and 81 is (3 × 3 × 7) and (3 × 3 × 3 × 3) respectively. As visible, 63 and 81 have common prime factors. Hence, the GCF of 63 and 81 is 3 × 3 = 9.

GCF of 63 and 81 by Long Division

GCF of 63 and 81 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 81 (larger number) by 63 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (63) by the remainder (18).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (9) is the GCF of 63 and 81.

GCF of 63 and 81 by Listing Common Factors

Factors of 63: 1, 3, 7, 9, 21, 63
Factors of 81: 1, 3, 9, 27, 81

There are 3 common factors of 63 and 81, that are 1, 3, and 9. Therefore, the greatest common factor of 63 and 81 is 9.

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GCF of 63 and 81 Examples

Example 1: For two numbers, GCF = 9 and LCM = 567. If one number is 63, find the other number.

Solution:

Given: GCF (y, 63) = 9 and LCM (y, 63) = 567
∵ GCF × LCM = 63 × (y)
⇒ y = (GCF × LCM)/63
⇒ y = (9 × 567)/63
⇒ y = 81
Therefore, the other number is 81.
Example 2: Find the GCF of 63 and 81, if their LCM is 567.

Solution:

∵ LCM × GCF = 63 × 81
⇒ GCF(63, 81) = (63 × 81)/567 = 9
Therefore, the greatest common factor of 63 and 81 is 9.
Example 3: Find the greatest number that divides 63 and 81 exactly.

Solution:

The greatest number that divides 63 and 81 exactly is their greatest common factor, i.e. GCF of 63 and 81.
⇒ Factors of 63 and 81:
- Factors of 63 = 1, 3, 7, 9, 21, 63
- Factors of 81 = 1, 3, 9, 27, 81
Therefore, the GCF of 63 and 81 is 9.

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FAQs on GCF of 63 and 81

What is the GCF of 63 and 81?

The GCF of 63 and 81 is 9. To calculate the greatest common factor of 63 and 81, we need to factor each number (factors of 63 = 1, 3, 7, 9, 21, 63; factors of 81 = 1, 3, 9, 27, 81) and choose the greatest factor that exactly divides both 63 and 81, i.e., 9.

What are the Methods to Find GCF of 63 and 81?

There are three commonly used methods to find the GCF of 63 and 81.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 63 and 81 by Long Division Method?

To find the GCF of 63, 81 using long division method, 81 is divided by 63. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

How to Find the GCF of 63 and 81 by Prime Factorization?

To find the GCF of 63 and 81, we will find the prime factorization of the given numbers, i.e. 63 = 3 × 3 × 7; 81 = 3 × 3 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 63 and 81. Hence, GCF(63, 81) = 3 × 3 = 9
☛ What is a Prime Number?

What is the Relation Between LCM and GCF of 63, 81?

The following equation can be used to express the relation between LCM and GCF of 63 and 81, i.e. GCF × LCM = 63 × 81.

If the GCF of 81 and 63 is 9, Find its LCM.

GCF(81, 63) × LCM(81, 63) = 81 × 63
Since the GCF of 81 and 63 = 9
⇒ 9 × LCM(81, 63) = 5103
Therefore, LCM = 567
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