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GCF of 90 and 120

GCF of 90 and 120 is the largest possible number that divides 90 and 120 exactly without any remainder. The factors of 90 and 120 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 and 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 respectively. There are 3 commonly used methods to find the GCF of 90 and 120 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 90 and 120
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 90 and 120?

Answer: GCF of 90 and 120 is 30.

Explanation:

The GCF of two non-zero integers, x(90) and y(120), is the greatest positive integer m(30) that divides both x(90) and y(120) without any remainder.

Methods to Find GCF of 90 and 120

Let's look at the different methods for finding the GCF of 90 and 120.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 90 and 120 by Listing Common Factors

Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

There are 8 common factors of 90 and 120, that are 1, 2, 3, 5, 6, 10, 15, and 30. Therefore, the greatest common factor of 90 and 120 is 30.

GCF of 90 and 120 by Long Division

GCF of 90 and 120 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 120 (larger number) by 90 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (90) by the remainder (30).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (30) is the GCF of 90 and 120.

GCF of 90 and 120 by Prime Factorization

Prime factorization of 90 and 120 is (2 × 3 × 3 × 5) and (2 × 2 × 2 × 3 × 5) respectively. As visible, 90 and 120 have common prime factors. Hence, the GCF of 90 and 120 is 2 × 3 × 5 = 30.

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GCF of 90 and 120 Examples

Example 1: For two numbers, GCF = 30 and LCM = 360. If one number is 90, find the other number.

Solution:

Given: GCF (z, 90) = 30 and LCM (z, 90) = 360
∵ GCF × LCM = 90 × (z)
⇒ z = (GCF × LCM)/90
⇒ z = (30 × 360)/90
⇒ z = 120
Therefore, the other number is 120.
Example 2: Find the GCF of 90 and 120, if their LCM is 360.

Solution:

∵ LCM × GCF = 90 × 120
⇒ GCF(90, 120) = (90 × 120)/360 = 30
Therefore, the greatest common factor of 90 and 120 is 30.
Example 3: Find the greatest number that divides 90 and 120 exactly.

Solution:

The greatest number that divides 90 and 120 exactly is their greatest common factor, i.e. GCF of 90 and 120.
⇒ Factors of 90 and 120:
- Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
- Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Therefore, the GCF of 90 and 120 is 30.

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FAQs on GCF of 90 and 120

What is the GCF of 90 and 120?

The GCF of 90 and 120 is 30. To calculate the GCF of 90 and 120, we need to factor each number (factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90; factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120) and choose the greatest factor that exactly divides both 90 and 120, i.e., 30.

How to Find the GCF of 90 and 120 by Prime Factorization?

To find the GCF of 90 and 120, we will find the prime factorization of the given numbers, i.e. 90 = 2 × 3 × 3 × 5; 120 = 2 × 2 × 2 × 3 × 5.
⇒ Since 2, 3, 5 are common terms in the prime factorization of 90 and 120. Hence, GCF(90, 120) = 2 × 3 × 5 = 30
☛ What are Prime Numbers?

How to Find the GCF of 90 and 120 by Long Division Method?

To find the GCF of 90, 120 using long division method, 120 is divided by 90. The corresponding divisor (30) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 90, 120?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 90 and 120, i.e. GCF × LCM = 90 × 120.

If the GCF of 120 and 90 is 30, Find its LCM.

GCF(120, 90) × LCM(120, 90) = 120 × 90
Since the GCF of 120 and 90 = 30
⇒ 30 × LCM(120, 90) = 10800
Therefore, LCM = 360
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 90 and 120?

There are three commonly used methods to find the GCF of 90 and 120.

By Long Division
By Prime Factorization
By Listing Common Factors

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