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GCF of 16 and 26

GCF of 16 and 26 is the largest possible number that divides 16 and 26 exactly without any remainder. The factors of 16 and 26 are 1, 2, 4, 8, 16 and 1, 2, 13, 26 respectively. There are 3 commonly used methods to find the GCF of 16 and 26 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 16 and 26
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16 and 26?

Answer: GCF of 16 and 26 is 2.

Explanation:

The GCF of two non-zero integers, x(16) and y(26), is the greatest positive integer m(2) that divides both x(16) and y(26) without any remainder.

Methods to Find GCF of 16 and 26

The methods to find the GCF of 16 and 26 are explained below.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

GCF of 16 and 26 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 26: 1, 2, 13, 26

There are 2 common factors of 16 and 26, that are 1 and 2. Therefore, the greatest common factor of 16 and 26 is 2.

GCF of 16 and 26 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 26 and Y = 16

GCF(26, 16) = GCF(16, 26 mod 16) = GCF(16, 10)
GCF(16, 10) = GCF(10, 16 mod 10) = GCF(10, 6)
GCF(10, 6) = GCF(6, 10 mod 6) = GCF(6, 4)
GCF(6, 4) = GCF(4, 6 mod 4) = GCF(4, 2)
GCF(4, 2) = GCF(2, 4 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 16 and 26 is 2.

GCF of 16 and 26 by Long Division

GCF of 16 and 26 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 26 (larger number) by 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (10).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 16 and 26.

☛ Also Check:

GCF of 16 and 26 Examples

Example 1: For two numbers, GCF = 2 and LCM = 208. If one number is 16, find the other number.

Solution:

Given: GCF (z, 16) = 2 and LCM (z, 16) = 208
∵ GCF × LCM = 16 × (z)
⇒ z = (GCF × LCM)/16
⇒ z = (2 × 208)/16
⇒ z = 26
Therefore, the other number is 26.
Example 2: Find the greatest number that divides 16 and 26 exactly.

Solution:

The greatest number that divides 16 and 26 exactly is their greatest common factor, i.e. GCF of 16 and 26.
⇒ Factors of 16 and 26:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 26 = 1, 2, 13, 26
Therefore, the GCF of 16 and 26 is 2.
Example 3: Find the GCF of 16 and 26, if their LCM is 208.

Solution:

∵ LCM × GCF = 16 × 26
⇒ GCF(16, 26) = (16 × 26)/208 = 2
Therefore, the greatest common factor of 16 and 26 is 2.

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FAQs on GCF of 16 and 26

What is the GCF of 16 and 26?

The GCF of 16 and 26 is 2. To calculate the greatest common factor (GCF) of 16 and 26, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 26 = 1, 2, 13, 26) and choose the greatest factor that exactly divides both 16 and 26, i.e., 2.

How to Find the GCF of 16 and 26 by Prime Factorization?

To find the GCF of 16 and 26, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 26 = 2 × 13.
⇒ Since 2 is the only common prime factor of 16 and 26. Hence, GCF (16, 26) = 2.
☛ Prime Numbers

If the GCF of 26 and 16 is 2, Find its LCM.

GCF(26, 16) × LCM(26, 16) = 26 × 16
Since the GCF of 26 and 16 = 2
⇒ 2 × LCM(26, 16) = 416
Therefore, LCM = 208
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 16, 26?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 16 and 26, i.e. GCF × LCM = 16 × 26.

What are the Methods to Find GCF of 16 and 26?

There are three commonly used methods to find the GCF of 16 and 26.

By Euclidean Algorithm
By Long Division
By Prime Factorization

How to Find the GCF of 16 and 26 by Long Division Method?

To find the GCF of 16, 26 using long division method, 26 is divided by 16. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

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