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GCF of 28 and 48

GCF of 28 and 48 is the largest possible number that divides 28 and 48 exactly without any remainder. The factors of 28 and 48 are 1, 2, 4, 7, 14, 28 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There are 3 commonly used methods to find the GCF of 28 and 48 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 28 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 28 and 48?

Answer: GCF of 28 and 48 is 4.

Explanation:

The GCF of two non-zero integers, x(28) and y(48), is the greatest positive integer m(4) that divides both x(28) and y(48) without any remainder.

Methods to Find GCF of 28 and 48

The methods to find the GCF of 28 and 48 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 28 and 48 by Prime Factorization

Prime factorization of 28 and 48 is (2 × 2 × 7) and (2 × 2 × 2 × 2 × 3) respectively. As visible, 28 and 48 have common prime factors. Hence, the GCF of 28 and 48 is 2 × 2 = 4.

GCF of 28 and 48 by Listing Common Factors

Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

There are 3 common factors of 28 and 48, that are 1, 2, and 4. Therefore, the greatest common factor of 28 and 48 is 4.

GCF of 28 and 48 by Long Division

GCF of 28 and 48 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 48 (larger number) by 28 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (28) by the remainder (20).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 28 and 48.

☛ Also Check:

GCF of 28 and 48 Examples

Example 1: Find the GCF of 28 and 48, if their LCM is 336.

Solution:

∵ LCM × GCF = 28 × 48
⇒ GCF(28, 48) = (28 × 48)/336 = 4
Therefore, the greatest common factor of 28 and 48 is 4.
Example 2: For two numbers, GCF = 4 and LCM = 336. If one number is 28, find the other number.

Solution:

Given: GCF (y, 28) = 4 and LCM (y, 28) = 336
∵ GCF × LCM = 28 × (y)
⇒ y = (GCF × LCM)/28
⇒ y = (4 × 336)/28
⇒ y = 48
Therefore, the other number is 48.
Example 3: The product of two numbers is 1344. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 1344
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1344/4
Therefore, the LCM is 336.

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FAQs on GCF of 28 and 48

What is the GCF of 28 and 48?

The GCF of 28 and 48 is 4. To calculate the greatest common factor (GCF) of 28 and 48, we need to factor each number (factors of 28 = 1, 2, 4, 7, 14, 28; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and choose the greatest factor that exactly divides both 28 and 48, i.e., 4.

How to Find the GCF of 28 and 48 by Prime Factorization?

To find the GCF of 28 and 48, we will find the prime factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 28 and 48. Hence, GCF(28, 48) = 2 × 2 = 4
☛ Prime Numbers

How to Find the GCF of 28 and 48 by Long Division Method?

To find the GCF of 28, 48 using long division method, 48 is divided by 28. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 28, 48?

The following equation can be used to express the relation between Least Common Multiple and GCF of 28 and 48, i.e. GCF × LCM = 28 × 48.

What are the Methods to Find GCF of 28 and 48?

There are three commonly used methods to find the GCF of 28 and 48.

By Euclidean Algorithm
By Long Division
By Prime Factorization

If the GCF of 48 and 28 is 4, Find its LCM.

GCF(48, 28) × LCM(48, 28) = 48 × 28
Since the GCF of 48 and 28 = 4
⇒ 4 × LCM(48, 28) = 1344
Therefore, LCM = 336
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