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GCF of 12 and 32

GCF of 12 and 32 is the largest possible number that divides 12 and 32 exactly without any remainder. The factors of 12 and 32 are 1, 2, 3, 4, 6, 12 and 1, 2, 4, 8, 16, 32 respectively. There are 3 commonly used methods to find the GCF of 12 and 32 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 12 and 32
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 32?

Answer: GCF of 12 and 32 is 4.

Explanation:

The GCF of two non-zero integers, x(12) and y(32), is the greatest positive integer m(4) that divides both x(12) and y(32) without any remainder.

Methods to Find GCF of 12 and 32

Let's look at the different methods for finding the GCF of 12 and 32.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 12 and 32 by Long Division

GCF of 12 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 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (8).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 12 and 32.

GCF of 12 and 32 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 32: 1, 2, 4, 8, 16, 32

There are 3 common factors of 12 and 32, that are 1, 2, and 4. Therefore, the greatest common factor of 12 and 32 is 4.

GCF of 12 and 32 by Prime Factorization

Prime factorization of 12 and 32 is (2 × 2 × 3) and (2 × 2 × 2 × 2 × 2) respectively. As visible, 12 and 32 have common prime factors. Hence, the GCF of 12 and 32 is 2 × 2 = 4.

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GCF of 12 and 32 Examples

Example 1: The product of two numbers is 384. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 384
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 384/4
Therefore, the LCM is 96.
Example 2: Find the greatest number that divides 12 and 32 exactly.

Solution:

The greatest number that divides 12 and 32 exactly is their greatest common factor, i.e. GCF of 12 and 32.
⇒ Factors of 12 and 32:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 32 = 1, 2, 4, 8, 16, 32
Therefore, the GCF of 12 and 32 is 4.
Example 3: Find the GCF of 12 and 32, if their LCM is 96.

Solution:

∵ LCM × GCF = 12 × 32
⇒ GCF(12, 32) = (12 × 32)/96 = 4
Therefore, the greatest common factor of 12 and 32 is 4.

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FAQs on GCF of 12 and 32

What is the GCF of 12 and 32?

The GCF of 12 and 32 is 4. To calculate the greatest common factor of 12 and 32, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 32 = 1, 2, 4, 8, 16, 32) and choose the greatest factor that exactly divides both 12 and 32, i.e., 4.

What are the Methods to Find GCF of 12 and 32?

There are three commonly used methods to find the GCF of 12 and 32.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 12 and 32 by Long Division Method?

To find the GCF of 12, 32 using long division method, 32 is divided by 12. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

How to Find the GCF of 12 and 32 by Prime Factorization?

To find the GCF of 12 and 32, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 32 = 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2 are common terms in the prime factorization of 12 and 32. Hence, GCF(12, 32) = 2 × 2 = 4
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 12, 32?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 12 and 32, i.e. GCF × LCM = 12 × 32.

If the GCF of 32 and 12 is 4, Find its LCM.

GCF(32, 12) × LCM(32, 12) = 32 × 12
Since the GCF of 32 and 12 = 4
⇒ 4 × LCM(32, 12) = 384
Therefore, LCM = 96
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