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GCF of 16 and 18

GCF of 16 and 18 is the largest possible number that divides 16 and 18 exactly without any remainder. The factors of 16 and 18 are 1, 2, 4, 8, 16 and 1, 2, 3, 6, 9, 18 respectively. There are 3 commonly used methods to find the GCF of 16 and 18 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 16 and 18
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16 and 18?

Answer: GCF of 16 and 18 is 2.

Explanation:

The GCF of two non-zero integers, x(16) and y(18), is the greatest positive integer m(2) that divides both x(16) and y(18) without any remainder.

Methods to Find GCF of 16 and 18

Let's look at the different methods for finding the GCF of 16 and 18.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 16 and 18 by Long Division

GCF of 16 and 18 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 18 (larger number) by 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 16 and 18.

GCF of 16 and 18 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 = 18 and Y = 16

GCF(18, 16) = GCF(16, 18 mod 16) = GCF(16, 2)
GCF(16, 2) = GCF(2, 16 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 16 and 18 is 2.

GCF of 16 and 18 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 18: 1, 2, 3, 6, 9, 18

There are 2 common factors of 16 and 18, that are 1 and 2. Therefore, the greatest common factor of 16 and 18 is 2.

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GCF of 16 and 18 Examples

Example 1: Find the GCF of 16 and 18, if their LCM is 144.

Solution:

∵ LCM × GCF = 16 × 18
⇒ GCF(16, 18) = (16 × 18)/144 = 2
Therefore, the greatest common factor of 16 and 18 is 2.
Example 2: For two numbers, GCF = 2 and LCM = 144. If one number is 18, find the other number.

Solution:

Given: GCF (x, 18) = 2 and LCM (x, 18) = 144
∵ GCF × LCM = 18 × (x)
⇒ x = (GCF × LCM)/18
⇒ x = (2 × 144)/18
⇒ x = 16
Therefore, the other number is 16.
Example 3: Find the greatest number that divides 16 and 18 exactly.

Solution:

The greatest number that divides 16 and 18 exactly is their greatest common factor, i.e. GCF of 16 and 18.
⇒ Factors of 16 and 18:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 18 = 1, 2, 3, 6, 9, 18
Therefore, the GCF of 16 and 18 is 2.

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FAQs on GCF of 16 and 18

What is the GCF of 16 and 18?

The GCF of 16 and 18 is 2. To calculate the greatest common factor of 16 and 18, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 18 = 1, 2, 3, 6, 9, 18) and choose the greatest factor that exactly divides both 16 and 18, i.e., 2.

What are the Methods to Find GCF of 16 and 18?

There are three commonly used methods to find the GCF of 16 and 18.

By Long Division
By Prime Factorization
By Listing Common Factors

If the GCF of 18 and 16 is 2, Find its LCM.

GCF(18, 16) × LCM(18, 16) = 18 × 16
Since the GCF of 18 and 16 = 2
⇒ 2 × LCM(18, 16) = 288
Therefore, LCM = 144
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How to Find the GCF of 16 and 18 by Long Division Method?

To find the GCF of 16, 18 using long division method, 18 is divided by 16. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

How to Find the GCF of 16 and 18 by Prime Factorization?

To find the GCF of 16 and 18, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 18 = 2 × 3 × 3.
⇒ Since 2 is the only common prime factor of 16 and 18. Hence, GCF (16, 18) = 2.
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 16, 18?

The following equation can be used to express the relation between Least Common Multiple and GCF of 16 and 18, i.e. GCF × LCM = 16 × 18.

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