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GCF of 16 and 25

GCF of 16 and 25 is the largest possible number that divides 16 and 25 exactly without any remainder. The factors of 16 and 25 are 1, 2, 4, 8, 16 and 1, 5, 25 respectively. There are 3 commonly used methods to find the GCF of 16 and 25 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 16 and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16 and 25?

Answer: GCF of 16 and 25 is 1.

Explanation:

The GCF of two non-zero integers, x(16) and y(25), is the greatest positive integer m(1) that divides both x(16) and y(25) without any remainder.

Methods to Find GCF of 16 and 25

Let's look at the different methods for finding the GCF of 16 and 25.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 16 and 25 by Long Division

GCF of 16 and 25 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 25 (larger number) by 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (9).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 16 and 25.

GCF of 16 and 25 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 25: 1, 5, 25

Since, 1 is the only common factor between 16 and 25. The Greatest Common Factor of 16 and 25 is 1.

GCF of 16 and 25 by Prime Factorization

Prime factorization of 16 and 25 is (2 × 2 × 2 × 2) and (5 × 5) respectively. As visible, there are no common prime factors between 16 and 25, i.e. they are co-prime. Hence, the GCF of 16 and 25 will be 1.

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GCF of 16 and 25 Examples

Example 1: The product of two numbers is 400. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 400
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 400/1
Therefore, the LCM is 400.
Example 2: Find the GCF of 16 and 25, if their LCM is 400.

Solution:

∵ LCM × GCF = 16 × 25
⇒ GCF(16, 25) = (16 × 25)/400 = 1
Therefore, the greatest common factor of 16 and 25 is 1.
Example 3: Find the greatest number that divides 16 and 25 exactly.

Solution:

The greatest number that divides 16 and 25 exactly is their greatest common factor, i.e. GCF of 16 and 25.
⇒ Factors of 16 and 25:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 25 = 1, 5, 25
Therefore, the GCF of 16 and 25 is 1.

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FAQs on GCF of 16 and 25

What is the GCF of 16 and 25?

The GCF of 16 and 25 is 1. To calculate the GCF (Greatest Common Factor) of 16 and 25, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 25 = 1, 5, 25) and choose the greatest factor that exactly divides both 16 and 25, i.e., 1.

If the GCF of 25 and 16 is 1, Find its LCM.

GCF(25, 16) × LCM(25, 16) = 25 × 16
Since the GCF of 25 and 16 = 1
⇒ 1 × LCM(25, 16) = 400
Therefore, LCM = 400
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 16 and 25?

There are three commonly used methods to find the GCF of 16 and 25.

By Euclidean Algorithm
By Prime Factorization
By Long Division

What is the Relation Between LCM and GCF of 16, 25?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 16 and 25, i.e. GCF × LCM = 16 × 25.

How to Find the GCF of 16 and 25 by Long Division Method?

To find the GCF of 16, 25 using long division method, 25 is divided by 16. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

How to Find the GCF of 16 and 25 by Prime Factorization?

To find the GCF of 16 and 25, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 25 = 5 × 5.
⇒ There is no common prime factor for 16 and 25. Hence, GCF (16, 25) = 1.
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