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GCF of 72 and 81

GCF of 72 and 81 is the largest possible number that divides 72 and 81 exactly without any remainder. The factors of 72 and 81 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 and 1, 3, 9, 27, 81 respectively. There are 3 commonly used methods to find the GCF of 72 and 81 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 72 and 81
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 72 and 81?

Answer: GCF of 72 and 81 is 9.

Explanation:

The GCF of two non-zero integers, x(72) and y(81), is the greatest positive integer m(9) that divides both x(72) and y(81) without any remainder.

Methods to Find GCF of 72 and 81

Let's look at the different methods for finding the GCF of 72 and 81.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 72 and 81 by Long Division

GCF of 72 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 72 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (72) by the remainder (9).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (9) is the GCF of 72 and 81.

GCF of 72 and 81 by Listing Common Factors

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 81: 1, 3, 9, 27, 81

There are 3 common factors of 72 and 81, that are 1, 3, and 9. Therefore, the greatest common factor of 72 and 81 is 9.

GCF of 72 and 81 by Prime Factorization

Prime factorization of 72 and 81 is (2 × 2 × 2 × 3 × 3) and (3 × 3 × 3 × 3) respectively. As visible, 72 and 81 have common prime factors. Hence, the GCF of 72 and 81 is 3 × 3 = 9.

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GCF of 72 and 81 Examples

Example 1: Find the greatest number that divides 72 and 81 exactly.

Solution:

The greatest number that divides 72 and 81 exactly is their greatest common factor, i.e. GCF of 72 and 81.
⇒ Factors of 72 and 81:
- Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Factors of 81 = 1, 3, 9, 27, 81
Therefore, the GCF of 72 and 81 is 9.
Example 2: For two numbers, GCF = 9 and LCM = 648. If one number is 72, find the other number.

Solution:

Given: GCF (x, 72) = 9 and LCM (x, 72) = 648
∵ GCF × LCM = 72 × (x)
⇒ x = (GCF × LCM)/72
⇒ x = (9 × 648)/72
⇒ x = 81
Therefore, the other number is 81.
Example 3: Find the GCF of 72 and 81, if their LCM is 648.

Solution:

∵ LCM × GCF = 72 × 81
⇒ GCF(72, 81) = (72 × 81)/648 = 9
Therefore, the greatest common factor of 72 and 81 is 9.

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FAQs on GCF of 72 and 81

What is the GCF of 72 and 81?

The GCF of 72 and 81 is 9. To calculate the greatest common factor (GCF) of 72 and 81, we need to factor each number (factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72; factors of 81 = 1, 3, 9, 27, 81) and choose the greatest factor that exactly divides both 72 and 81, i.e., 9.

What are the Methods to Find GCF of 72 and 81?

There are three commonly used methods to find the GCF of 72 and 81.

By Long Division
By Prime Factorization
By Euclidean Algorithm

If the GCF of 81 and 72 is 9, Find its LCM.

GCF(81, 72) × LCM(81, 72) = 81 × 72
Since the GCF of 81 and 72 = 9
⇒ 9 × LCM(81, 72) = 5832
Therefore, LCM = 648
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How to Find the GCF of 72 and 81 by Long Division Method?

To find the GCF of 72, 81 using long division method, 81 is divided by 72. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 72, 81?

The following equation can be used to express the relation between Least Common Multiple and GCF of 72 and 81, i.e. GCF × LCM = 72 × 81.

How to Find the GCF of 72 and 81 by Prime Factorization?

To find the GCF of 72 and 81, we will find the prime factorization of the given numbers, i.e. 72 = 2 × 2 × 2 × 3 × 3; 81 = 3 × 3 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 72 and 81. Hence, GCF(72, 81) = 3 × 3 = 9
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