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GCF of 16 and 28

GCF of 16 and 28 is the largest possible number that divides 16 and 28 exactly without any remainder. The factors of 16 and 28 are 1, 2, 4, 8, 16 and 1, 2, 4, 7, 14, 28 respectively. There are 3 commonly used methods to find the GCF of 16 and 28 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 16 and 28
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16 and 28?

Answer: GCF of 16 and 28 is 4.

Explanation:

The GCF of two non-zero integers, x(16) and y(28), is the greatest positive integer m(4) that divides both x(16) and y(28) without any remainder.

Methods to Find GCF of 16 and 28

The methods to find the GCF of 16 and 28 are explained below.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 16 and 28 by Long Division

GCF of 16 and 28 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 28 (larger number) by 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 16 and 28.

GCF of 16 and 28 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 28: 1, 2, 4, 7, 14, 28

There are 3 common factors of 16 and 28, that are 1, 2, and 4. Therefore, the greatest common factor of 16 and 28 is 4.

GCF of 16 and 28 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 = 28 and Y = 16

GCF(28, 16) = GCF(16, 28 mod 16) = GCF(16, 12)
GCF(16, 12) = GCF(12, 16 mod 12) = GCF(12, 4)
GCF(12, 4) = GCF(4, 12 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 16 and 28 is 4.

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GCF of 16 and 28 Examples

Example 1: Find the GCF of 16 and 28, if their LCM is 112.

Solution:

∵ LCM × GCF = 16 × 28
⇒ GCF(16, 28) = (16 × 28)/112 = 4
Therefore, the greatest common factor of 16 and 28 is 4.
Example 2: Find the greatest number that divides 16 and 28 exactly.

Solution:

The greatest number that divides 16 and 28 exactly is their greatest common factor, i.e. GCF of 16 and 28.
⇒ Factors of 16 and 28:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 28 = 1, 2, 4, 7, 14, 28
Therefore, the GCF of 16 and 28 is 4.
Example 3: For two numbers, GCF = 4 and LCM = 112. If one number is 28, find the other number.

Solution:

Given: GCF (y, 28) = 4 and LCM (y, 28) = 112
∵ GCF × LCM = 28 × (y)
⇒ y = (GCF × LCM)/28
⇒ y = (4 × 112)/28
⇒ y = 16
Therefore, the other number is 16.

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FAQs on GCF of 16 and 28

What is the GCF of 16 and 28?

The GCF of 16 and 28 is 4. To calculate the greatest common factor (GCF) of 16 and 28, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the greatest factor that exactly divides both 16 and 28, i.e., 4.

How to Find the GCF of 16 and 28 by Prime Factorization?

To find the GCF of 16 and 28, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 28 = 2 × 2 × 7.
⇒ Since 2, 2 are common terms in the prime factorization of 16 and 28. Hence, GCF(16, 28) = 2 × 2 = 4
☛ What is a Prime Number?

What are the Methods to Find GCF of 16 and 28?

There are three commonly used methods to find the GCF of 16 and 28.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the GCF of 16 and 28 by Long Division Method?

To find the GCF of 16, 28 using long division method, 28 is divided by 16. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 16, 28?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 16 and 28, i.e. GCF × LCM = 16 × 28.

If the GCF of 28 and 16 is 4, Find its LCM.

GCF(28, 16) × LCM(28, 16) = 28 × 16
Since the GCF of 28 and 16 = 4
⇒ 4 × LCM(28, 16) = 448
Therefore, LCM = 112
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