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GCF of 80 and 90

GCF of 80 and 90 is the largest possible number that divides 80 and 90 exactly without any remainder. The factors of 80 and 90 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 respectively. There are 3 commonly used methods to find the GCF of 80 and 90 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 80 and 90
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 80 and 90?

Answer: GCF of 80 and 90 is 10.

Explanation:

The GCF of two non-zero integers, x(80) and y(90), is the greatest positive integer m(10) that divides both x(80) and y(90) without any remainder.

Methods to Find GCF of 80 and 90

The methods to find the GCF of 80 and 90 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 80 and 90 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 = 90 and Y = 80

GCF(90, 80) = GCF(80, 90 mod 80) = GCF(80, 10)
GCF(80, 10) = GCF(10, 80 mod 10) = GCF(10, 0)
GCF(10, 0) = 10 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 80 and 90 is 10.

GCF of 80 and 90 by Long Division

GCF of 80 and 90 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 90 (larger number) by 80 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (80) by the remainder (10).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (10) is the GCF of 80 and 90.

GCF of 80 and 90 by Listing Common Factors

Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

There are 4 common factors of 80 and 90, that are 1, 2, 10, and 5. Therefore, the greatest common factor of 80 and 90 is 10.

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GCF of 80 and 90 Examples

Example 1: Find the GCF of 80 and 90, if their LCM is 720.

Solution:

∵ LCM × GCF = 80 × 90
⇒ GCF(80, 90) = (80 × 90)/720 = 10
Therefore, the greatest common factor of 80 and 90 is 10.
Example 2: Find the greatest number that divides 80 and 90 exactly.

Solution:

The greatest number that divides 80 and 90 exactly is their greatest common factor, i.e. GCF of 80 and 90.
⇒ Factors of 80 and 90:
- Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
- Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Therefore, the GCF of 80 and 90 is 10.
Example 3: The product of two numbers is 7200. If their GCF is 10, what is their LCM?

Solution:

Given: GCF = 10 and product of numbers = 7200
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 7200/10
Therefore, the LCM is 720.

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FAQs on GCF of 80 and 90

What is the GCF of 80 and 90?

The GCF of 80 and 90 is 10. To calculate the greatest common factor of 80 and 90, we need to factor each number (factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80; factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90) and choose the greatest factor that exactly divides both 80 and 90, i.e., 10.

How to Find the GCF of 80 and 90 by Prime Factorization?

To find the GCF of 80 and 90, we will find the prime factorization of the given numbers, i.e. 80 = 2 × 2 × 2 × 2 × 5; 90 = 2 × 3 × 3 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 80 and 90. Hence, GCF(80, 90) = 2 × 5 = 10
☛ What is a Prime Number?

How to Find the GCF of 80 and 90 by Long Division Method?

To find the GCF of 80, 90 using long division method, 90 is divided by 80. The corresponding divisor (10) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 80 and 90?

There are three commonly used methods to find the GCF of 80 and 90.

By Long Division
By Listing Common Factors
By Prime Factorization

What is the Relation Between LCM and GCF of 80, 90?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 80 and 90, i.e. GCF × LCM = 80 × 90.

If the GCF of 90 and 80 is 10, Find its LCM.

GCF(90, 80) × LCM(90, 80) = 90 × 80
Since the GCF of 90 and 80 = 10
⇒ 10 × LCM(90, 80) = 7200
Therefore, LCM = 720
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