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GCF of 30 and 80

GCF of 30 and 80 is the largest possible number that divides 30 and 80 exactly without any remainder. The factors of 30 and 80 are 1, 2, 3, 5, 6, 10, 15, 30 and 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 respectively. There are 3 commonly used methods to find the GCF of 30 and 80 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 30 and 80
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 30 and 80?

Answer: GCF of 30 and 80 is 10.

Explanation:

The GCF of two non-zero integers, x(30) and y(80), is the greatest positive integer m(10) that divides both x(30) and y(80) without any remainder.

Methods to Find GCF of 30 and 80

The methods to find the GCF of 30 and 80 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 30 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 = 30

GCF(80, 30) = GCF(30, 80 mod 30) = GCF(30, 20)
GCF(30, 20) = GCF(20, 30 mod 20) = GCF(20, 10)
GCF(20, 10) = GCF(10, 20 mod 10) = GCF(10, 0)
GCF(10, 0) = 10 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 30 and 80 is 10.

GCF of 30 and 80 by Long Division

GCF of 30 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 30 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (30) by the remainder (20).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (10) is the GCF of 30 and 80.

GCF of 30 and 80 by Listing Common Factors

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

There are 4 common factors of 30 and 80, that are 1, 2, 10, and 5. Therefore, the greatest common factor of 30 and 80 is 10.

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GCF of 30 and 80 Examples

Example 1: The product of two numbers is 2400. If their GCF is 10, what is their LCM?

Solution:

Given: GCF = 10 and product of numbers = 2400
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2400/10
Therefore, the LCM is 240.
Example 2: For two numbers, GCF = 10 and LCM = 240. If one number is 30, find the other number.

Solution:

Given: GCF (x, 30) = 10 and LCM (x, 30) = 240
∵ GCF × LCM = 30 × (x)
⇒ x = (GCF × LCM)/30
⇒ x = (10 × 240)/30
⇒ x = 80
Therefore, the other number is 80.
Example 3: Find the GCF of 30 and 80, if their LCM is 240.

Solution:

∵ LCM × GCF = 30 × 80
⇒ GCF(30, 80) = (30 × 80)/240 = 10
Therefore, the greatest common factor of 30 and 80 is 10.

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FAQs on GCF of 30 and 80

What is the GCF of 30 and 80?

The GCF of 30 and 80 is 10. To calculate the greatest common factor of 30 and 80, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80) and choose the greatest factor that exactly divides both 30 and 80, i.e., 10.

If the GCF of 80 and 30 is 10, Find its LCM.

GCF(80, 30) × LCM(80, 30) = 80 × 30
Since the GCF of 80 and 30 = 10
⇒ 10 × LCM(80, 30) = 2400
Therefore, LCM = 240
☛ GCF Calculator

How to Find the GCF of 30 and 80 by Long Division Method?

To find the GCF of 30, 80 using long division method, 80 is divided by 30. The corresponding divisor (10) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 30, 80?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 30 and 80, i.e. GCF × LCM = 30 × 80.

How to Find the GCF of 30 and 80 by Prime Factorization?

To find the GCF of 30 and 80, we will find the prime factorization of the given numbers, i.e. 30 = 2 × 3 × 5; 80 = 2 × 2 × 2 × 2 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 30 and 80. Hence, GCF(30, 80) = 2 × 5 = 10
☛ Prime Number

What are the Methods to Find GCF of 30 and 80?

There are three commonly used methods to find the GCF of 30 and 80.

By Prime Factorization
By Listing Common Factors
By Long Division

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