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GCF of 75 and 90

GCF of 75 and 90 is the largest possible number that divides 75 and 90 exactly without any remainder. The factors of 75 and 90 are 1, 3, 5, 15, 25, 75 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 75 and 90 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 75 and 90
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 75 and 90?

Answer: GCF of 75 and 90 is 15.

Explanation:

The GCF of two non-zero integers, x(75) and y(90), is the greatest positive integer m(15) that divides both x(75) and y(90) without any remainder.

Methods to Find GCF of 75 and 90

The methods to find the GCF of 75 and 90 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 75 and 90 by Listing Common Factors

Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

There are 4 common factors of 75 and 90, that are 1, 3, 5, and 15. Therefore, the greatest common factor of 75 and 90 is 15.

GCF of 75 and 90 by Prime Factorization

Prime factorization of 75 and 90 is (3 × 5 × 5) and (2 × 3 × 3 × 5) respectively. As visible, 75 and 90 have common prime factors. Hence, the GCF of 75 and 90 is 3 × 5 = 15.

GCF of 75 and 90 by Long Division

GCF of 75 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 75 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (75) by the remainder (15).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (15) is the GCF of 75 and 90.

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GCF of 75 and 90 Examples

Example 1: The product of two numbers is 6750. If their GCF is 15, what is their LCM?

Solution:

Given: GCF = 15 and product of numbers = 6750
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 6750/15
Therefore, the LCM is 450.
Example 2: Find the greatest number that divides 75 and 90 exactly.

Solution:

The greatest number that divides 75 and 90 exactly is their greatest common factor, i.e. GCF of 75 and 90.
⇒ Factors of 75 and 90:
- Factors of 75 = 1, 3, 5, 15, 25, 75
- Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Therefore, the GCF of 75 and 90 is 15.
Example 3: For two numbers, GCF = 15 and LCM = 450. If one number is 90, find the other number.

Solution:

Given: GCF (x, 90) = 15 and LCM (x, 90) = 450
∵ GCF × LCM = 90 × (x)
⇒ x = (GCF × LCM)/90
⇒ x = (15 × 450)/90
⇒ x = 75
Therefore, the other number is 75.

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FAQs on GCF of 75 and 90

What is the GCF of 75 and 90?

The GCF of 75 and 90 is 15. To calculate the greatest common factor (GCF) of 75 and 90, we need to factor each number (factors of 75 = 1, 3, 5, 15, 25, 75; factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90) and choose the greatest factor that exactly divides both 75 and 90, i.e., 15.

If the GCF of 90 and 75 is 15, Find its LCM.

GCF(90, 75) × LCM(90, 75) = 90 × 75
Since the GCF of 90 and 75 = 15
⇒ 15 × LCM(90, 75) = 6750
Therefore, LCM = 450
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 75, 90?

The following equation can be used to express the relation between LCM and GCF of 75 and 90, i.e. GCF × LCM = 75 × 90.

What are the Methods to Find GCF of 75 and 90?

There are three commonly used methods to find the GCF of 75 and 90.

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the GCF of 75 and 90 by Long Division Method?

To find the GCF of 75, 90 using long division method, 90 is divided by 75. The corresponding divisor (15) when remainder equals 0 is taken as GCF.

How to Find the GCF of 75 and 90 by Prime Factorization?

To find the GCF of 75 and 90, we will find the prime factorization of the given numbers, i.e. 75 = 3 × 5 × 5; 90 = 2 × 3 × 3 × 5.
⇒ Since 3, 5 are common terms in the prime factorization of 75 and 90. Hence, GCF(75, 90) = 3 × 5 = 15
☛ What are Prime Numbers?

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