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GCF of 10 and 16

GCF of 10 and 16 is the largest possible number that divides 10 and 16 exactly without any remainder. The factors of 10 and 16 are 1, 2, 5, 10 and 1, 2, 4, 8, 16 respectively. There are 3 commonly used methods to find the GCF of 10 and 16 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 10 and 16
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 10 and 16?

Answer: GCF of 10 and 16 is 2.

Explanation:

The GCF of two non-zero integers, x(10) and y(16), is the greatest positive integer m(2) that divides both x(10) and y(16) without any remainder.

Methods to Find GCF of 10 and 16

Let's look at the different methods for finding the GCF of 10 and 16.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 10 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 = 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 10 and 16 is 2.

GCF of 10 and 16 by Long Division

GCF of 10 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 10 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (10) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 10 and 16.

GCF of 10 and 16 by Prime Factorization

Prime factorization of 10 and 16 is (2 × 5) and (2 × 2 × 2 × 2) respectively. As visible, 10 and 16 have only one common prime factor i.e. 2. Hence, the GCF of 10 and 16 is 2.

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GCF of 10 and 16 Examples

Example 1: Find the GCF of 10 and 16, if their LCM is 80.

Solution:

∵ LCM × GCF = 10 × 16
⇒ GCF(10, 16) = (10 × 16)/80 = 2
Therefore, the greatest common factor of 10 and 16 is 2.
Example 2: Find the greatest number that divides 10 and 16 exactly.

Solution:

The greatest number that divides 10 and 16 exactly is their greatest common factor, i.e. GCF of 10 and 16.
⇒ Factors of 10 and 16:
- Factors of 10 = 1, 2, 5, 10
- Factors of 16 = 1, 2, 4, 8, 16
Therefore, the GCF of 10 and 16 is 2.
Example 3: The product of two numbers is 160. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 160
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 160/2
Therefore, the LCM is 80.

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FAQs on GCF of 10 and 16

What is the GCF of 10 and 16?

The GCF of 10 and 16 is 2. To calculate the GCF of 10 and 16, we need to factor each number (factors of 10 = 1, 2, 5, 10; factors of 16 = 1, 2, 4, 8, 16) and choose the greatest factor that exactly divides both 10 and 16, i.e., 2.

How to Find the GCF of 10 and 16 by Long Division Method?

To find the GCF of 10, 16 using long division method, 16 is divided by 10. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

If the GCF of 16 and 10 is 2, Find its LCM.

GCF(16, 10) × LCM(16, 10) = 16 × 10
Since the GCF of 16 and 10 = 2
⇒ 2 × LCM(16, 10) = 160
Therefore, LCM = 80
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What is the Relation Between LCM and GCF of 10, 16?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 10 and 16, i.e. GCF × LCM = 10 × 16.

What are the Methods to Find GCF of 10 and 16?

There are three commonly used methods to find the GCF of 10 and 16.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the GCF of 10 and 16 by Prime Factorization?

To find the GCF of 10 and 16, we will find the prime factorization of the given numbers, i.e. 10 = 2 × 5; 16 = 2 × 2 × 2 × 2.
⇒ Since 2 is the only common prime factor of 10 and 16. Hence, GCF (10, 16) = 2.
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