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GCF of 8 and 16

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

1.	GCF of 8 and 16
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 8 and 16?

Answer: GCF of 8 and 16 is 8.

Explanation:

The GCF of two non-zero integers, x(8) and y(16), is the greatest positive integer m(8) that divides both x(8) and y(16) without any remainder.

Methods to Find GCF of 8 and 16

Let's look at the different methods for finding the GCF of 8 and 16.

Prime Factorization Method
Using Euclid's Algorithm
Long Division Method

GCF of 8 and 16 by Prime Factorization

Prime factorization of 8 and 16 is (2 × 2 × 2) and (2 × 2 × 2 × 2) respectively. As visible, 8 and 16 have common prime factors. Hence, the GCF of 8 and 16 is 2 × 2 × 2 = 8.

GCF of 8 and 16 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 = 16 and Y = 8

GCF(16, 8) = GCF(8, 16 mod 8) = GCF(8, 0)
GCF(8, 0) = 8 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 8 and 16 is 8.

GCF of 8 and 16 by Long Division

GCF of 8 and 16 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 16 (larger number) by 8 (smaller number).
Step 2: Since the remainder = 0, the divisor (8) is the GCF of 8 and 16.

The corresponding divisor (8) is the GCF of 8 and 16.

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GCF of 8 and 16 Examples

Example 1: For two numbers, GCF = 8 and LCM = 16. If one number is 8, find the other number.

Solution:

Given: GCF (y, 8) = 8 and LCM (y, 8) = 16
∵ GCF × LCM = 8 × (y)
⇒ y = (GCF × LCM)/8
⇒ y = (8 × 16)/8
⇒ y = 16
Therefore, the other number is 16.
Example 2: The product of two numbers is 128. If their GCF is 8, what is their LCM?

Solution:

Given: GCF = 8 and product of numbers = 128
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 128/8
Therefore, the LCM is 16.
Example 3: Find the greatest number that divides 8 and 16 exactly.

Solution:

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

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FAQs on GCF of 8 and 16

What is the GCF of 8 and 16?

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

What is the Relation Between LCM and GCF of 8, 16?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 8 and 16, i.e. GCF × LCM = 8 × 16.

How to Find the GCF of 8 and 16 by Prime Factorization?

To find the GCF of 8 and 16, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 16 = 2 × 2 × 2 × 2.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 8 and 16. Hence, GCF(8, 16) = 2 × 2 × 2 = 8
☛ What is a Prime Number?

How to Find the GCF of 8 and 16 by Long Division Method?

To find the GCF of 8, 16 using long division method, 16 is divided by 8. The corresponding divisor (8) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 8 and 16?

There are three commonly used methods to find the GCF of 8 and 16.

By Prime Factorization
By Euclidean Algorithm
By Long Division

If the GCF of 16 and 8 is 8, Find its LCM.

GCF(16, 8) × LCM(16, 8) = 16 × 8
Since the GCF of 16 and 8 = 8
⇒ 8 × LCM(16, 8) = 128
Therefore, LCM = 16
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