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GCF of 6 and 16

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

1.	GCF of 6 and 16
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 6 and 16?

Answer: GCF of 6 and 16 is 2.

Explanation:

The GCF of two non-zero integers, x(6) and y(16), is the greatest positive integer m(2) that divides both x(6) and y(16) without any remainder.

Methods to Find GCF of 6 and 16

Let's look at the different methods for finding the GCF of 6 and 16.

Prime Factorization Method
Using Euclid's Algorithm
Long Division Method

GCF of 6 and 16 by Prime Factorization

Prime factorization of 6 and 16 is (2 × 3) and (2 × 2 × 2 × 2) respectively. As visible, 6 and 16 have only one common prime factor i.e. 2. Hence, the GCF of 6 and 16 is 2.

GCF of 6 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 = 6

GCF(16, 6) = GCF(6, 16 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 6 and 16 is 2.

GCF of 6 and 16 by Long Division

GCF of 6 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 6 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (6) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 6 and 16.

☛ Also Check:

GCF of 6 and 16 Examples

Example 1: Find the GCF of 6 and 16, if their LCM is 48.

Solution:

∵ LCM × GCF = 6 × 16
⇒ GCF(6, 16) = (6 × 16)/48 = 2
Therefore, the greatest common factor of 6 and 16 is 2.
Example 2: The product of two numbers is 96. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 96
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 96/2
Therefore, the LCM is 48.
Example 3: For two numbers, GCF = 2 and LCM = 48. If one number is 16, find the other number.

Solution:

Given: GCF (z, 16) = 2 and LCM (z, 16) = 48
∵ GCF × LCM = 16 × (z)
⇒ z = (GCF × LCM)/16
⇒ z = (2 × 48)/16
⇒ z = 6
Therefore, the other number is 6.

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FAQs on GCF of 6 and 16

What is the GCF of 6 and 16?

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

What are the Methods to Find GCF of 6 and 16?

There are three commonly used methods to find the GCF of 6 and 16.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 6 and 16 by Prime Factorization?

To find the GCF of 6 and 16, we will find the prime factorization of the given numbers, i.e. 6 = 2 × 3; 16 = 2 × 2 × 2 × 2.
⇒ Since 2 is the only common prime factor of 6 and 16. Hence, GCF (6, 16) = 2.
☛ What are Prime Numbers?

If the GCF of 16 and 6 is 2, Find its LCM.

GCF(16, 6) × LCM(16, 6) = 16 × 6
Since the GCF of 16 and 6 = 2
⇒ 2 × LCM(16, 6) = 96
Therefore, LCM = 48
☛ GCF Calculator

What is the Relation Between LCM and GCF of 6, 16?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 6 and 16, i.e. GCF × LCM = 6 × 16.

How to Find the GCF of 6 and 16 by Long Division Method?

To find the GCF of 6, 16 using long division method, 16 is divided by 6. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

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