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GCF of 20 and 48

GCF of 20 and 48 is the largest possible number that divides 20 and 48 exactly without any remainder. The factors of 20 and 48 are 1, 2, 4, 5, 10, 20 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There are 3 commonly used methods to find the GCF of 20 and 48 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 20 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 20 and 48?

Answer: GCF of 20 and 48 is 4.

Explanation:

The GCF of two non-zero integers, x(20) and y(48), is the greatest positive integer m(4) that divides both x(20) and y(48) without any remainder.

Methods to Find GCF of 20 and 48

The methods to find the GCF of 20 and 48 are explained below.

Prime Factorization Method
Using Euclid's Algorithm
Long Division Method

GCF of 20 and 48 by Prime Factorization

Prime factorization of 20 and 48 is (2 × 2 × 5) and (2 × 2 × 2 × 2 × 3) respectively. As visible, 20 and 48 have common prime factors. Hence, the GCF of 20 and 48 is 2 × 2 = 4.

GCF of 20 and 48 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 48 and Y = 20

GCF(48, 20) = GCF(20, 48 mod 20) = GCF(20, 8)
GCF(20, 8) = GCF(8, 20 mod 8) = GCF(8, 4)
GCF(8, 4) = GCF(4, 8 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 20 and 48 is 4.

GCF of 20 and 48 by Long Division

GCF of 20 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 20 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (8).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 20 and 48.

☛ Also Check:

GCF of 20 and 48 Examples

Example 1: Find the GCF of 20 and 48, if their LCM is 240.

Solution:

∵ LCM × GCF = 20 × 48
⇒ GCF(20, 48) = (20 × 48)/240 = 4
Therefore, the greatest common factor of 20 and 48 is 4.
Example 2: The product of two numbers is 960. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 960
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 960/4
Therefore, the LCM is 240.
Example 3: For two numbers, GCF = 4 and LCM = 240. If one number is 20, find the other number.

Solution:

Given: GCF (x, 20) = 4 and LCM (x, 20) = 240
∵ GCF × LCM = 20 × (x)
⇒ x = (GCF × LCM)/20
⇒ x = (4 × 240)/20
⇒ x = 48
Therefore, the other number is 48.

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FAQs on GCF of 20 and 48

What is the GCF of 20 and 48?

The GCF of 20 and 48 is 4. To calculate the greatest common factor of 20 and 48, we need to factor each number (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and choose the greatest factor that exactly divides both 20 and 48, i.e., 4.

How to Find the GCF of 20 and 48 by Long Division Method?

To find the GCF of 20, 48 using long division method, 48 is divided by 20. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 20 and 48?

There are three commonly used methods to find the GCF of 20 and 48.

By Prime Factorization
By Long Division
By Euclidean Algorithm

If the GCF of 48 and 20 is 4, Find its LCM.

GCF(48, 20) × LCM(48, 20) = 48 × 20
Since the GCF of 48 and 20 = 4
⇒ 4 × LCM(48, 20) = 960
Therefore, LCM = 240
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What is the Relation Between LCM and GCF of 20, 48?

The following equation can be used to express the relation between Least Common Multiple and GCF of 20 and 48, i.e. GCF × LCM = 20 × 48.

How to Find the GCF of 20 and 48 by Prime Factorization?

To find the GCF of 20 and 48, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 20 and 48. Hence, GCF(20, 48) = 2 × 2 = 4
☛ Prime Number

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