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GCF of 16 and 100

GCF of 16 and 100 is the largest possible number that divides 16 and 100 exactly without any remainder. The factors of 16 and 100 are 1, 2, 4, 8, 16 and 1, 2, 4, 5, 10, 20, 25, 50, 100 respectively. There are 3 commonly used methods to find the GCF of 16 and 100 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 16 and 100
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16 and 100?

Answer: GCF of 16 and 100 is 4.

Explanation:

The GCF of two non-zero integers, x(16) and y(100), is the greatest positive integer m(4) that divides both x(16) and y(100) without any remainder.

Methods to Find GCF of 16 and 100

The methods to find the GCF of 16 and 100 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 16 and 100 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

There are 3 common factors of 16 and 100, that are 1, 2, and 4. Therefore, the greatest common factor of 16 and 100 is 4.

GCF of 16 and 100 by Prime Factorization

Prime factorization of 16 and 100 is (2 × 2 × 2 × 2) and (2 × 2 × 5 × 5) respectively. As visible, 16 and 100 have common prime factors. Hence, the GCF of 16 and 100 is 2 × 2 = 4.

GCF of 16 and 100 by Long Division

GCF of 16 and 100 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 100 (larger number) by 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 16 and 100.

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GCF of 16 and 100 Examples

Example 1: The product of two numbers is 1600. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 1600
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1600/4
Therefore, the LCM is 400.
Example 2: Find the greatest number that divides 16 and 100 exactly.

Solution:

The greatest number that divides 16 and 100 exactly is their greatest common factor, i.e. GCF of 16 and 100.
⇒ Factors of 16 and 100:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
Therefore, the GCF of 16 and 100 is 4.
Example 3: Find the GCF of 16 and 100, if their LCM is 400.

Solution:

∵ LCM × GCF = 16 × 100
⇒ GCF(16, 100) = (16 × 100)/400 = 4
Therefore, the greatest common factor of 16 and 100 is 4.

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FAQs on GCF of 16 and 100

What is the GCF of 16 and 100?

The GCF of 16 and 100 is 4. To calculate the GCF of 16 and 100, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100) and choose the greatest factor that exactly divides both 16 and 100, i.e., 4.

What are the Methods to Find GCF of 16 and 100?

There are three commonly used methods to find the GCF of 16 and 100.

By Euclidean Algorithm
By Prime Factorization
By Long Division

What is the Relation Between LCM and GCF of 16, 100?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 16 and 100, i.e. GCF × LCM = 16 × 100.

If the GCF of 100 and 16 is 4, Find its LCM.

GCF(100, 16) × LCM(100, 16) = 100 × 16
Since the GCF of 100 and 16 = 4
⇒ 4 × LCM(100, 16) = 1600
Therefore, LCM = 400
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How to Find the GCF of 16 and 100 by Prime Factorization?

To find the GCF of 16 and 100, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 100 = 2 × 2 × 5 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 16 and 100. Hence, GCF(16, 100) = 2 × 2 = 4
☛ What is a Prime Number?

How to Find the GCF of 16 and 100 by Long Division Method?

To find the GCF of 16, 100 using long division method, 100 is divided by 16. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

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