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GCF of 25 and 40

GCF of 25 and 40 is the largest possible number that divides 25 and 40 exactly without any remainder. The factors of 25 and 40 are 1, 5, 25 and 1, 2, 4, 5, 8, 10, 20, 40 respectively. There are 3 commonly used methods to find the GCF of 25 and 40 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 25 and 40
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 25 and 40?

Answer: GCF of 25 and 40 is 5.

Explanation:

The GCF of two non-zero integers, x(25) and y(40), is the greatest positive integer m(5) that divides both x(25) and y(40) without any remainder.

Methods to Find GCF of 25 and 40

Let's look at the different methods for finding the GCF of 25 and 40.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 25 and 40 by Long Division

GCF of 25 and 40 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 40 (larger number) by 25 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (25) by the remainder (15).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 25 and 40.

GCF of 25 and 40 by Listing Common Factors

Factors of 25: 1, 5, 25
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

There are 2 common factors of 25 and 40, that are 1 and 5. Therefore, the greatest common factor of 25 and 40 is 5.

GCF of 25 and 40 by Prime Factorization

Prime factorization of 25 and 40 is (5 × 5) and (2 × 2 × 2 × 5) respectively. As visible, 25 and 40 have only one common prime factor i.e. 5. Hence, the GCF of 25 and 40 is 5.

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GCF of 25 and 40 Examples

Example 1: Find the greatest number that divides 25 and 40 exactly.

Solution:

The greatest number that divides 25 and 40 exactly is their greatest common factor, i.e. GCF of 25 and 40.
⇒ Factors of 25 and 40:
- Factors of 25 = 1, 5, 25
- Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
Therefore, the GCF of 25 and 40 is 5.
Example 2: Find the GCF of 25 and 40, if their LCM is 200.

Solution:

∵ LCM × GCF = 25 × 40
⇒ GCF(25, 40) = (25 × 40)/200 = 5
Therefore, the greatest common factor of 25 and 40 is 5.
Example 3: The product of two numbers is 1000. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 1000
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1000/5
Therefore, the LCM is 200.

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FAQs on GCF of 25 and 40

What is the GCF of 25 and 40?

The GCF of 25 and 40 is 5. To calculate the GCF of 25 and 40, we need to factor each number (factors of 25 = 1, 5, 25; factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the greatest factor that exactly divides both 25 and 40, i.e., 5.

What are the Methods to Find GCF of 25 and 40?

There are three commonly used methods to find the GCF of 25 and 40.

By Prime Factorization
By Long Division
By Listing Common Factors

If the GCF of 40 and 25 is 5, Find its LCM.

GCF(40, 25) × LCM(40, 25) = 40 × 25
Since the GCF of 40 and 25 = 5
⇒ 5 × LCM(40, 25) = 1000
Therefore, LCM = 200
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What is the Relation Between LCM and GCF of 25, 40?

The following equation can be used to express the relation between LCM and GCF of 25 and 40, i.e. GCF × LCM = 25 × 40.

How to Find the GCF of 25 and 40 by Long Division Method?

To find the GCF of 25, 40 using long division method, 40 is divided by 25. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

How to Find the GCF of 25 and 40 by Prime Factorization?

To find the GCF of 25 and 40, we will find the prime factorization of the given numbers, i.e. 25 = 5 × 5; 40 = 2 × 2 × 2 × 5.
⇒ Since 5 is the only common prime factor of 25 and 40. Hence, GCF (25, 40) = 5.
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