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GCF of 14 and 48

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

1.	GCF of 14 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 14 and 48?

Answer: GCF of 14 and 48 is 2.

Explanation:

The GCF of two non-zero integers, x(14) and y(48), is the greatest positive integer m(2) that divides both x(14) and y(48) without any remainder.

Methods to Find GCF of 14 and 48

Let's look at the different methods for finding the GCF of 14 and 48.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 14 and 48 by Prime Factorization

Prime factorization of 14 and 48 is (2 × 7) and (2 × 2 × 2 × 2 × 3) respectively. As visible, 14 and 48 have only one common prime factor i.e. 2. Hence, the GCF of 14 and 48 is 2.

GCF of 14 and 48 by Long Division

GCF of 14 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 14 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (14) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 14 and 48.

GCF of 14 and 48 by Listing Common Factors

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

There are 2 common factors of 14 and 48, that are 1 and 2. Therefore, the greatest common factor of 14 and 48 is 2.

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GCF of 14 and 48 Examples

Example 1: Find the greatest number that divides 14 and 48 exactly.

Solution:

The greatest number that divides 14 and 48 exactly is their greatest common factor, i.e. GCF of 14 and 48.
⇒ Factors of 14 and 48:
- Factors of 14 = 1, 2, 7, 14
- Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Therefore, the GCF of 14 and 48 is 2.
Example 2: Find the GCF of 14 and 48, if their LCM is 336.

Solution:

∵ LCM × GCF = 14 × 48
⇒ GCF(14, 48) = (14 × 48)/336 = 2
Therefore, the greatest common factor of 14 and 48 is 2.
Example 3: The product of two numbers is 672. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 672
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 672/2
Therefore, the LCM is 336.

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FAQs on GCF of 14 and 48

What is the GCF of 14 and 48?

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

If the GCF of 48 and 14 is 2, Find its LCM.

GCF(48, 14) × LCM(48, 14) = 48 × 14
Since the GCF of 48 and 14 = 2
⇒ 2 × LCM(48, 14) = 672
Therefore, LCM = 336
☛ Greatest Common Factor Calculator

How to Find the GCF of 14 and 48 by Prime Factorization?

To find the GCF of 14 and 48, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2 is the only common prime factor of 14 and 48. Hence, GCF (14, 48) = 2.
☛ What is a Prime Number?

What are the Methods to Find GCF of 14 and 48?

There are three commonly used methods to find the GCF of 14 and 48.

By Prime Factorization
By Long Division
By Listing Common Factors

What is the Relation Between LCM and GCF of 14, 48?

The following equation can be used to express the relation between Least Common Multiple and GCF of 14 and 48, i.e. GCF × LCM = 14 × 48.

How to Find the GCF of 14 and 48 by Long Division Method?

To find the GCF of 14, 48 using long division method, 48 is divided by 14. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

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