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GCF of 48 and 16

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

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

What is GCF of 48 and 16?

Answer: GCF of 48 and 16 is 16.

Explanation:

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

Methods to Find GCF of 48 and 16

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

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 48 and 16 by Prime Factorization

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

GCF of 48 and 16 by Listing Common Factors

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

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

GCF of 48 and 16 by Long Division

GCF of 48 and 16 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 48 and 16.

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

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GCF of 48 and 16 Examples

Example 1: Find the GCF of 48 and 16, if their LCM is 48.

Solution:

∵ LCM × GCF = 48 × 16
⇒ GCF(48, 16) = (48 × 16)/48 = 16
Therefore, the greatest common factor of 48 and 16 is 16.
Example 2: 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.
Example 3: For two numbers, GCF = 16 and LCM = 48. If one number is 48, find the other number.

Solution:

Given: GCF (y, 48) = 16 and LCM (y, 48) = 48
∵ GCF × LCM = 48 × (y)
⇒ y = (GCF × LCM)/48
⇒ y = (16 × 48)/48
⇒ y = 16
Therefore, the other number is 16.

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FAQs on GCF of 48 and 16

What is the GCF of 48 and 16?

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

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

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

By Listing Common Factors
By Long Division
By Prime Factorization

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

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

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

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

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

GCF(16, 48) × LCM(16, 48) = 16 × 48
Since the GCF of 16 and 48 = 16
⇒ 16 × LCM(16, 48) = 768
Therefore, LCM = 48
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How to Find the GCF of 48 and 16 by Prime Factorization?

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

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