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

GCF of 25 and 60

GCF of 25 and 60 is the largest possible number that divides 25 and 60 exactly without any remainder. The factors of 25 and 60 are 1, 5, 25 and 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 respectively. There are 3 commonly used methods to find the GCF of 25 and 60 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 25 and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 25 and 60?

Answer: GCF of 25 and 60 is 5.

Explanation:

The GCF of two non-zero integers, x(25) and y(60), is the greatest positive integer m(5) that divides both x(25) and y(60) without any remainder.

Methods to Find GCF of 25 and 60

Let's look at the different methods for finding the GCF of 25 and 60.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 25 and 60 by Listing Common Factors

Factors of 25: 1, 5, 25
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

There are 2 common factors of 25 and 60, that are 1 and 5. Therefore, the greatest common factor of 25 and 60 is 5.

GCF of 25 and 60 by Prime Factorization

Prime factorization of 25 and 60 is (5 × 5) and (2 × 2 × 3 × 5) respectively. As visible, 25 and 60 have only one common prime factor i.e. 5. Hence, the GCF of 25 and 60 is 5.

GCF of 25 and 60 by Long Division

GCF of 25 and 60 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 60 (larger number) by 25 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (25) by the remainder (10).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 25 and 60.

☛ Also Check:

GCF of 25 and 60 Examples

Example 1: Find the GCF of 25 and 60, if their LCM is 300.

Solution:

∵ LCM × GCF = 25 × 60
⇒ GCF(25, 60) = (25 × 60)/300 = 5
Therefore, the greatest common factor of 25 and 60 is 5.
Example 2: The product of two numbers is 1500. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 1500
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1500/5
Therefore, the LCM is 300.
Example 3: For two numbers, GCF = 5 and LCM = 300. If one number is 60, find the other number.

Solution:

Given: GCF (y, 60) = 5 and LCM (y, 60) = 300
∵ GCF × LCM = 60 × (y)
⇒ y = (GCF × LCM)/60
⇒ y = (5 × 300)/60
⇒ y = 25
Therefore, the other number is 25.

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 25 and 60

What is the GCF of 25 and 60?

The GCF of 25 and 60 is 5. To calculate the greatest common factor (GCF) of 25 and 60, we need to factor each number (factors of 25 = 1, 5, 25; factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) and choose the greatest factor that exactly divides both 25 and 60, i.e., 5.

What are the Methods to Find GCF of 25 and 60?

There are three commonly used methods to find the GCF of 25 and 60.

By Prime Factorization
By Euclidean Algorithm
By Long Division

What is the Relation Between LCM and GCF of 25, 60?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 25 and 60, i.e. GCF × LCM = 25 × 60.

How to Find the GCF of 25 and 60 by Prime Factorization?

To find the GCF of 25 and 60, we will find the prime factorization of the given numbers, i.e. 25 = 5 × 5; 60 = 2 × 2 × 3 × 5.
⇒ Since 5 is the only common prime factor of 25 and 60. Hence, GCF (25, 60) = 5.
☛ What are Prime Numbers?

If the GCF of 60 and 25 is 5, Find its LCM.

GCF(60, 25) × LCM(60, 25) = 60 × 25
Since the GCF of 60 and 25 = 5
⇒ 5 × LCM(60, 25) = 1500
Therefore, LCM = 300
☛ GCF Calculator

How to Find the GCF of 25 and 60 by Long Division Method?

To find the GCF of 25, 60 using long division method, 60 is divided by 25. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum