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GCF of 20 and 32

GCF of 20 and 32 is the largest possible number that divides 20 and 32 exactly without any remainder. The factors of 20 and 32 are 1, 2, 4, 5, 10, 20 and 1, 2, 4, 8, 16, 32 respectively. There are 3 commonly used methods to find the GCF of 20 and 32 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 20 and 32
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 20 and 32?

Answer: GCF of 20 and 32 is 4.

Explanation:

The GCF of two non-zero integers, x(20) and y(32), is the greatest positive integer m(4) that divides both x(20) and y(32) without any remainder.

Methods to Find GCF of 20 and 32

The methods to find the GCF of 20 and 32 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 20 and 32 by Prime Factorization

Prime factorization of 20 and 32 is (2 × 2 × 5) and (2 × 2 × 2 × 2 × 2) respectively. As visible, 20 and 32 have common prime factors. Hence, the GCF of 20 and 32 is 2 × 2 = 4.

GCF of 20 and 32 by Listing Common Factors

Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 32: 1, 2, 4, 8, 16, 32

There are 3 common factors of 20 and 32, that are 1, 2, and 4. Therefore, the greatest common factor of 20 and 32 is 4.

GCF of 20 and 32 by Long Division

GCF of 20 and 32 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 32 (larger number) by 20 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 20 and 32.

☛ Also Check:

GCF of 20 and 32 Examples

Example 1: For two numbers, GCF = 4 and LCM = 160. If one number is 32, find the other number.

Solution:

Given: GCF (x, 32) = 4 and LCM (x, 32) = 160
∵ GCF × LCM = 32 × (x)
⇒ x = (GCF × LCM)/32
⇒ x = (4 × 160)/32
⇒ x = 20
Therefore, the other number is 20.
Example 2: Find the greatest number that divides 20 and 32 exactly.

Solution:

The greatest number that divides 20 and 32 exactly is their greatest common factor, i.e. GCF of 20 and 32.
⇒ Factors of 20 and 32:
- Factors of 20 = 1, 2, 4, 5, 10, 20
- Factors of 32 = 1, 2, 4, 8, 16, 32
Therefore, the GCF of 20 and 32 is 4.
Example 3: Find the GCF of 20 and 32, if their LCM is 160.

Solution:

∵ LCM × GCF = 20 × 32
⇒ GCF(20, 32) = (20 × 32)/160 = 4
Therefore, the greatest common factor of 20 and 32 is 4.

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FAQs on GCF of 20 and 32

What is the GCF of 20 and 32?

The GCF of 20 and 32 is 4. To calculate the greatest common factor (GCF) of 20 and 32, we need to factor each number (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 32 = 1, 2, 4, 8, 16, 32) and choose the greatest factor that exactly divides both 20 and 32, i.e., 4.

How to Find the GCF of 20 and 32 by Long Division Method?

To find the GCF of 20, 32 using long division method, 32 is divided by 20. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

How to Find the GCF of 20 and 32 by Prime Factorization?

To find the GCF of 20 and 32, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 32 = 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2 are common terms in the prime factorization of 20 and 32. Hence, GCF(20, 32) = 2 × 2 = 4
☛ Prime Number

What is the Relation Between LCM and GCF of 20, 32?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 20 and 32, i.e. GCF × LCM = 20 × 32.

What are the Methods to Find GCF of 20 and 32?

There are three commonly used methods to find the GCF of 20 and 32.

By Long Division
By Prime Factorization
By Euclidean Algorithm

If the GCF of 32 and 20 is 4, Find its LCM.

GCF(32, 20) × LCM(32, 20) = 32 × 20
Since the GCF of 32 and 20 = 4
⇒ 4 × LCM(32, 20) = 640
Therefore, LCM = 160
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