A day full of math games & activities. Find one near you.

GCF of 45 and 75

GCF of 45 and 75 is the largest possible number that divides 45 and 75 exactly without any remainder. The factors of 45 and 75 are 1, 3, 5, 9, 15, 45 and 1, 3, 5, 15, 25, 75 respectively. There are 3 commonly used methods to find the GCF of 45 and 75 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 45 and 75
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 45 and 75?

Answer: GCF of 45 and 75 is 15.

Explanation:

The GCF of two non-zero integers, x(45) and y(75), is the greatest positive integer m(15) that divides both x(45) and y(75) without any remainder.

Methods to Find GCF of 45 and 75

The methods to find the GCF of 45 and 75 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 45 and 75 by Listing Common Factors

Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 75: 1, 3, 5, 15, 25, 75

There are 4 common factors of 45 and 75, that are 1, 3, 5, and 15. Therefore, the greatest common factor of 45 and 75 is 15.

GCF of 45 and 75 by Prime Factorization

Prime factorization of 45 and 75 is (3 × 3 × 5) and (3 × 5 × 5) respectively. As visible, 45 and 75 have common prime factors. Hence, the GCF of 45 and 75 is 3 × 5 = 15.

GCF of 45 and 75 by Long Division

GCF of 45 and 75 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 75 (larger number) by 45 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (45) by the remainder (30).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (15) is the GCF of 45 and 75.

☛ Also Check:

GCF of 45 and 75 Examples

Example 1: Find the greatest number that divides 45 and 75 exactly.

Solution:

The greatest number that divides 45 and 75 exactly is their greatest common factor, i.e. GCF of 45 and 75.
⇒ Factors of 45 and 75:
- Factors of 45 = 1, 3, 5, 9, 15, 45
- Factors of 75 = 1, 3, 5, 15, 25, 75
Therefore, the GCF of 45 and 75 is 15.
Example 2: The product of two numbers is 3375. If their GCF is 15, what is their LCM?

Solution:

Given: GCF = 15 and product of numbers = 3375
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 3375/15
Therefore, the LCM is 225.
Example 3: For two numbers, GCF = 15 and LCM = 225. If one number is 75, find the other number.

Solution:

Given: GCF (x, 75) = 15 and LCM (x, 75) = 225
∵ GCF × LCM = 75 × (x)
⇒ x = (GCF × LCM)/75
⇒ x = (15 × 225)/75
⇒ x = 45
Therefore, the other number is 45.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 45 and 75

What is the GCF of 45 and 75?

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

What are the Methods to Find GCF of 45 and 75?

There are three commonly used methods to find the GCF of 45 and 75.

By Prime Factorization
By Long Division
By Listing Common Factors

If the GCF of 75 and 45 is 15, Find its LCM.

GCF(75, 45) × LCM(75, 45) = 75 × 45
Since the GCF of 75 and 45 = 15
⇒ 15 × LCM(75, 45) = 3375
Therefore, LCM = 225
☛ Greatest Common Factor Calculator

How to Find the GCF of 45 and 75 by Prime Factorization?

To find the GCF of 45 and 75, we will find the prime factorization of the given numbers, i.e. 45 = 3 × 3 × 5; 75 = 3 × 5 × 5.
⇒ Since 3, 5 are common terms in the prime factorization of 45 and 75. Hence, GCF(45, 75) = 3 × 5 = 15
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 45, 75?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 45 and 75, i.e. GCF × LCM = 45 × 75.

How to Find the GCF of 45 and 75 by Long Division Method?

To find the GCF of 45, 75 using long division method, 75 is divided by 45. The corresponding divisor (15) when remainder equals 0 is taken as GCF.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum