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GCF of 32 and 81

GCF of 32 and 81 is the largest possible number that divides 32 and 81 exactly without any remainder. The factors of 32 and 81 are 1, 2, 4, 8, 16, 32 and 1, 3, 9, 27, 81 respectively. There are 3 commonly used methods to find the GCF of 32 and 81 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 32 and 81
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 32 and 81?

Answer: GCF of 32 and 81 is 1.

Explanation:

The GCF of two non-zero integers, x(32) and y(81), is the greatest positive integer m(1) that divides both x(32) and y(81) without any remainder.

Methods to Find GCF of 32 and 81

The methods to find the GCF of 32 and 81 are explained below.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 32 and 81 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 = 81 and Y = 32

GCF(81, 32) = GCF(32, 81 mod 32) = GCF(32, 17)
GCF(32, 17) = GCF(17, 32 mod 17) = GCF(17, 15)
GCF(17, 15) = GCF(15, 17 mod 15) = GCF(15, 2)
GCF(15, 2) = GCF(2, 15 mod 2) = GCF(2, 1)
GCF(2, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 32 and 81 is 1.

GCF of 32 and 81 by Long Division

GCF of 32 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 32 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (32) by the remainder (17).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 32 and 81.

GCF of 32 and 81 by Prime Factorization

Prime factorization of 32 and 81 is (2 × 2 × 2 × 2 × 2) and (3 × 3 × 3 × 3) respectively. As visible, there are no common prime factors between 32 and 81, i.e. they are co-prime. Hence, the GCF of 32 and 81 will be 1.

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GCF of 32 and 81 Examples

Example 1: Find the greatest number that divides 32 and 81 exactly.

Solution:

The greatest number that divides 32 and 81 exactly is their greatest common factor, i.e. GCF of 32 and 81.
⇒ Factors of 32 and 81:
- Factors of 32 = 1, 2, 4, 8, 16, 32
- Factors of 81 = 1, 3, 9, 27, 81
Therefore, the GCF of 32 and 81 is 1.
Example 2: For two numbers, GCF = 1 and LCM = 2592. If one number is 32, find the other number.

Solution:

Given: GCF (z, 32) = 1 and LCM (z, 32) = 2592
∵ GCF × LCM = 32 × (z)
⇒ z = (GCF × LCM)/32
⇒ z = (1 × 2592)/32
⇒ z = 81
Therefore, the other number is 81.
Example 3: The product of two numbers is 2592. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 2592
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2592/1
Therefore, the LCM is 2592.

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FAQs on GCF of 32 and 81

What is the GCF of 32 and 81?

The GCF of 32 and 81 is 1. To calculate the GCF of 32 and 81, we need to factor each number (factors of 32 = 1, 2, 4, 8, 16, 32; factors of 81 = 1, 3, 9, 27, 81) and choose the greatest factor that exactly divides both 32 and 81, i.e., 1.

How to Find the GCF of 32 and 81 by Prime Factorization?

To find the GCF of 32 and 81, we will find the prime factorization of the given numbers, i.e. 32 = 2 × 2 × 2 × 2 × 2; 81 = 3 × 3 × 3 × 3.
⇒ There is no common prime factor for 32 and 81. Hence, GCF (32, 81) = 1.
☛ Prime Number

What is the Relation Between LCM and GCF of 32, 81?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 32 and 81, i.e. GCF × LCM = 32 × 81.

If the GCF of 81 and 32 is 1, Find its LCM.

GCF(81, 32) × LCM(81, 32) = 81 × 32
Since the GCF of 81 and 32 = 1
⇒ 1 × LCM(81, 32) = 2592
Therefore, LCM = 2592
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How to Find the GCF of 32 and 81 by Long Division Method?

To find the GCF of 32, 81 using long division method, 81 is divided by 32. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 32 and 81?

There are three commonly used methods to find the GCF of 32 and 81.

By Long Division
By Prime Factorization
By Listing Common Factors

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