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

GCF of 75 and 125

GCF of 75 and 125 is the largest possible number that divides 75 and 125 exactly without any remainder. The factors of 75 and 125 are 1, 3, 5, 15, 25, 75 and 1, 5, 25, 125 respectively. There are 3 commonly used methods to find the GCF of 75 and 125 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 75 and 125
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 75 and 125?

Answer: GCF of 75 and 125 is 25.

Explanation:

The GCF of two non-zero integers, x(75) and y(125), is the greatest positive integer m(25) that divides both x(75) and y(125) without any remainder.

Methods to Find GCF of 75 and 125

Let's look at the different methods for finding the GCF of 75 and 125.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 75 and 125 by Long Division

GCF of 75 and 125 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 125 (larger number) by 75 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (75) by the remainder (50).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (25) is the GCF of 75 and 125.

GCF of 75 and 125 by Listing Common Factors

Factors of 75: 1, 3, 5, 15, 25, 75
Factors of 125: 1, 5, 25, 125

There are 3 common factors of 75 and 125, that are 1, 5, and 25. Therefore, the greatest common factor of 75 and 125 is 25.

GCF of 75 and 125 by Prime Factorization

Prime factorization of 75 and 125 is (3 × 5 × 5) and (5 × 5 × 5) respectively. As visible, 75 and 125 have common prime factors. Hence, the GCF of 75 and 125 is 5 × 5 = 25.

☛ Also Check:

GCF of 75 and 125 Examples

Example 1: For two numbers, GCF = 25 and LCM = 375. If one number is 75, find the other number.

Solution:

Given: GCF (y, 75) = 25 and LCM (y, 75) = 375
∵ GCF × LCM = 75 × (y)
⇒ y = (GCF × LCM)/75
⇒ y = (25 × 375)/75
⇒ y = 125
Therefore, the other number is 125.
Example 2: Find the greatest number that divides 75 and 125 exactly.

Solution:

The greatest number that divides 75 and 125 exactly is their greatest common factor, i.e. GCF of 75 and 125.
⇒ Factors of 75 and 125:
- Factors of 75 = 1, 3, 5, 15, 25, 75
- Factors of 125 = 1, 5, 25, 125
Therefore, the GCF of 75 and 125 is 25.
Example 3: The product of two numbers is 9375. If their GCF is 25, what is their LCM?

Solution:

Given: GCF = 25 and product of numbers = 9375
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 9375/25
Therefore, the LCM is 375.

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 75 and 125

What is the GCF of 75 and 125?

The GCF of 75 and 125 is 25. To calculate the greatest common factor (GCF) of 75 and 125, we need to factor each number (factors of 75 = 1, 3, 5, 15, 25, 75; factors of 125 = 1, 5, 25, 125) and choose the greatest factor that exactly divides both 75 and 125, i.e., 25.

How to Find the GCF of 75 and 125 by Long Division Method?

To find the GCF of 75, 125 using long division method, 125 is divided by 75. The corresponding divisor (25) when remainder equals 0 is taken as GCF.

If the GCF of 125 and 75 is 25, Find its LCM.

GCF(125, 75) × LCM(125, 75) = 125 × 75
Since the GCF of 125 and 75 = 25
⇒ 25 × LCM(125, 75) = 9375
Therefore, LCM = 375
☛ GCF Calculator

How to Find the GCF of 75 and 125 by Prime Factorization?

To find the GCF of 75 and 125, we will find the prime factorization of the given numbers, i.e. 75 = 3 × 5 × 5; 125 = 5 × 5 × 5.
⇒ Since 5, 5 are common terms in the prime factorization of 75 and 125. Hence, GCF(75, 125) = 5 × 5 = 25
☛ Prime Number

What is the Relation Between LCM and GCF of 75, 125?

The following equation can be used to express the relation between LCM and GCF of 75 and 125, i.e. GCF × LCM = 75 × 125.

What are the Methods to Find GCF of 75 and 125?

There are three commonly used methods to find the GCF of 75 and 125.

By Euclidean Algorithm
By Long Division
By Prime Factorization

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum