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GCF of 16 and 48

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

1.	GCF of 16 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16 and 48?

Answer: GCF of 16 and 48 is 16.

Explanation:

The GCF of two non-zero integers, x(16) and y(48), is the greatest positive integer m(16) that divides both x(16) and y(48) without any remainder.

Methods to Find GCF of 16 and 48

Let's look at the different methods for finding the GCF of 16 and 48.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 16 and 48 by Long Division

GCF of 16 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 16 (smaller number).
Step 2: Since the remainder = 0, the divisor (16) is the GCF of 16 and 48.

The corresponding divisor (16) is the GCF of 16 and 48.

GCF of 16 and 48 by Listing Common Factors

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

There are 5 common factors of 16 and 48, that are 1, 2, 4, 8, and 16. Therefore, the greatest common factor of 16 and 48 is 16.

GCF of 16 and 48 by Prime Factorization

Prime factorization of 16 and 48 is (2 × 2 × 2 × 2) and (2 × 2 × 2 × 2 × 3) respectively. As visible, 16 and 48 have common prime factors. Hence, the GCF of 16 and 48 is 2 × 2 × 2 × 2 = 16.

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GCF of 16 and 48 Examples

Example 1: Find the greatest number that divides 16 and 48 exactly.

Solution:

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

Solution:

∵ LCM × GCF = 16 × 48
⇒ GCF(16, 48) = (16 × 48)/48 = 16
Therefore, the greatest common factor of 16 and 48 is 16.
Example 3: The product of two numbers is 768. If their GCF is 16, what is their LCM?

Solution:

Given: GCF = 16 and product of numbers = 768
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 768/16
Therefore, the LCM is 48.

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FAQs on GCF of 16 and 48

What is the GCF of 16 and 48?

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

How to Find the GCF of 16 and 48 by Long Division Method?

To find the GCF of 16, 48 using long division method, 48 is divided by 16. The corresponding divisor (16) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 16, 48?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 16 and 48, i.e. GCF × LCM = 16 × 48.

How to Find the GCF of 16 and 48 by Prime Factorization?

To find the GCF of 16 and 48, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2, 2, 2 are common terms in the prime factorization of 16 and 48. Hence, GCF(16, 48) = 2 × 2 × 2 × 2 = 16
☛ What is a Prime Number?

What are the Methods to Find GCF of 16 and 48?

There are three commonly used methods to find the GCF of 16 and 48.

By Prime Factorization
By Listing Common Factors
By Long Division

If the GCF of 48 and 16 is 16, Find its LCM.

GCF(48, 16) × LCM(48, 16) = 48 × 16
Since the GCF of 48 and 16 = 16
⇒ 16 × LCM(48, 16) = 768
Therefore, LCM = 48
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