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GCF of 32 and 80

GCF of 32 and 80 is the largest possible number that divides 32 and 80 exactly without any remainder. The factors of 32 and 80 are 1, 2, 4, 8, 16, 32 and 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 respectively. There are 3 commonly used methods to find the GCF of 32 and 80 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 32 and 80
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 32 and 80?

Answer: GCF of 32 and 80 is 16.

Explanation:

The GCF of two non-zero integers, x(32) and y(80), is the greatest positive integer m(16) that divides both x(32) and y(80) without any remainder.

Methods to Find GCF of 32 and 80

The methods to find the GCF of 32 and 80 are explained below.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

GCF of 32 and 80 by Prime Factorization

Prime factorization of 32 and 80 is (2 × 2 × 2 × 2 × 2) and (2 × 2 × 2 × 2 × 5) respectively. As visible, 32 and 80 have common prime factors. Hence, the GCF of 32 and 80 is 2 × 2 × 2 × 2 = 16.

GCF of 32 and 80 by Long Division

GCF of 32 and 80 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 80 (larger number) by 32 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (32) by the remainder (16).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (16) is the GCF of 32 and 80.

GCF of 32 and 80 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 = 80 and Y = 32

GCF(80, 32) = GCF(32, 80 mod 32) = GCF(32, 16)
GCF(32, 16) = GCF(16, 32 mod 16) = GCF(16, 0)
GCF(16, 0) = 16 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 32 and 80 is 16.

☛ Also Check:

GCF of 32 and 80 Examples

Example 1: The product of two numbers is 2560. If their GCF is 16, what is their LCM?

Solution:

Given: GCF = 16 and product of numbers = 2560
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2560/16
Therefore, the LCM is 160.
Example 2: For two numbers, GCF = 16 and LCM = 160. If one number is 80, find the other number.

Solution:

Given: GCF (y, 80) = 16 and LCM (y, 80) = 160
∵ GCF × LCM = 80 × (y)
⇒ y = (GCF × LCM)/80
⇒ y = (16 × 160)/80
⇒ y = 32
Therefore, the other number is 32.
Example 3: Find the GCF of 32 and 80, if their LCM is 160.

Solution:

∵ LCM × GCF = 32 × 80
⇒ GCF(32, 80) = (32 × 80)/160 = 16
Therefore, the greatest common factor of 32 and 80 is 16.

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FAQs on GCF of 32 and 80

What is the GCF of 32 and 80?

The GCF of 32 and 80 is 16. To calculate the greatest common factor (GCF) of 32 and 80, we need to factor each number (factors of 32 = 1, 2, 4, 8, 16, 32; factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80) and choose the greatest factor that exactly divides both 32 and 80, i.e., 16.

What are the Methods to Find GCF of 32 and 80?

There are three commonly used methods to find the GCF of 32 and 80.

By Long Division
By Listing Common Factors
By Prime Factorization

How to Find the GCF of 32 and 80 by Prime Factorization?

To find the GCF of 32 and 80, we will find the prime factorization of the given numbers, i.e. 32 = 2 × 2 × 2 × 2 × 2; 80 = 2 × 2 × 2 × 2 × 5.
⇒ Since 2, 2, 2, 2 are common terms in the prime factorization of 32 and 80. Hence, GCF(32, 80) = 2 × 2 × 2 × 2 = 16
☛ What is a Prime Number?

If the GCF of 80 and 32 is 16, Find its LCM.

GCF(80, 32) × LCM(80, 32) = 80 × 32
Since the GCF of 80 and 32 = 16
⇒ 16 × LCM(80, 32) = 2560
Therefore, LCM = 160
☛ GCF Calculator

What is the Relation Between LCM and GCF of 32, 80?

The following equation can be used to express the relation between LCM and GCF of 32 and 80, i.e. GCF × LCM = 32 × 80.

How to Find the GCF of 32 and 80 by Long Division Method?

To find the GCF of 32, 80 using long division method, 80 is divided by 32. The corresponding divisor (16) when remainder equals 0 is taken as GCF.

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