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GCF of 12 and 28

GCF of 12 and 28 is the largest possible number that divides 12 and 28 exactly without any remainder. The factors of 12 and 28 are 1, 2, 3, 4, 6, 12 and 1, 2, 4, 7, 14, 28 respectively. There are 3 commonly used methods to find the GCF of 12 and 28 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 12 and 28
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 28?

Answer: GCF of 12 and 28 is 4.

Explanation:

The GCF of two non-zero integers, x(12) and y(28), is the greatest positive integer m(4) that divides both x(12) and y(28) without any remainder.

Methods to Find GCF of 12 and 28

Let's look at the different methods for finding the GCF of 12 and 28.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 12 and 28 by Prime Factorization

Prime factorization of 12 and 28 is (2 × 2 × 3) and (2 × 2 × 7) respectively. As visible, 12 and 28 have common prime factors. Hence, the GCF of 12 and 28 is 2 × 2 = 4.

GCF of 12 and 28 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 28: 1, 2, 4, 7, 14, 28

There are 3 common factors of 12 and 28, that are 1, 2, and 4. Therefore, the greatest common factor of 12 and 28 is 4.

GCF of 12 and 28 by Long Division

GCF of 12 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 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 12 and 28.

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GCF of 12 and 28 Examples

Example 1: Find the greatest number that divides 12 and 28 exactly.

Solution:

The greatest number that divides 12 and 28 exactly is their greatest common factor, i.e. GCF of 12 and 28.
⇒ Factors of 12 and 28:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 28 = 1, 2, 4, 7, 14, 28
Therefore, the GCF of 12 and 28 is 4.
Example 2: For two numbers, GCF = 4 and LCM = 84. If one number is 12, find the other number.

Solution:

Given: GCF (y, 12) = 4 and LCM (y, 12) = 84
∵ GCF × LCM = 12 × (y)
⇒ y = (GCF × LCM)/12
⇒ y = (4 × 84)/12
⇒ y = 28
Therefore, the other number is 28.
Example 3: Find the GCF of 12 and 28, if their LCM is 84.

Solution:

∵ LCM × GCF = 12 × 28
⇒ GCF(12, 28) = (12 × 28)/84 = 4
Therefore, the greatest common factor of 12 and 28 is 4.

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FAQs on GCF of 12 and 28

What is the GCF of 12 and 28?

The GCF of 12 and 28 is 4. To calculate the GCF (Greatest Common Factor) of 12 and 28, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the greatest factor that exactly divides both 12 and 28, i.e., 4.

What is the Relation Between LCM and GCF of 12, 28?

The following equation can be used to express the relation between Least Common Multiple and GCF of 12 and 28, i.e. GCF × LCM = 12 × 28.

What are the Methods to Find GCF of 12 and 28?

There are three commonly used methods to find the GCF of 12 and 28.

By Long Division
By Prime Factorization
By Listing Common Factors

If the GCF of 28 and 12 is 4, Find its LCM.

GCF(28, 12) × LCM(28, 12) = 28 × 12
Since the GCF of 28 and 12 = 4
⇒ 4 × LCM(28, 12) = 336
Therefore, LCM = 84
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How to Find the GCF of 12 and 28 by Long Division Method?

To find the GCF of 12, 28 using long division method, 28 is divided by 12. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

How to Find the GCF of 12 and 28 by Prime Factorization?

To find the GCF of 12 and 28, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 28 = 2 × 2 × 7.
⇒ Since 2, 2 are common terms in the prime factorization of 12 and 28. Hence, GCF(12, 28) = 2 × 2 = 4
☛ What are Prime Numbers?

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