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GCF of 12 and 40

GCF of 12 and 40 is the largest possible number that divides 12 and 40 exactly without any remainder. The factors of 12 and 40 are 1, 2, 3, 4, 6, 12 and 1, 2, 4, 5, 8, 10, 20, 40 respectively. There are 3 commonly used methods to find the GCF of 12 and 40 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 12 and 40
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 40?

Answer: GCF of 12 and 40 is 4.

Explanation:

The GCF of two non-zero integers, x(12) and y(40), is the greatest positive integer m(4) that divides both x(12) and y(40) without any remainder.

Methods to Find GCF of 12 and 40

Let's look at the different methods for finding the GCF of 12 and 40.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 12 and 40 by Prime Factorization

Prime factorization of 12 and 40 is (2 × 2 × 3) and (2 × 2 × 2 × 5) respectively. As visible, 12 and 40 have common prime factors. Hence, the GCF of 12 and 40 is 2 × 2 = 4.

GCF of 12 and 40 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

There are 3 common factors of 12 and 40, that are 1, 2, and 4. Therefore, the greatest common factor of 12 and 40 is 4.

GCF of 12 and 40 by Long Division

GCF of 12 and 40 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 40 (larger number) by 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 12 and 40.

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GCF of 12 and 40 Examples

Example 1: Find the greatest number that divides 12 and 40 exactly.

Solution:

The greatest number that divides 12 and 40 exactly is their greatest common factor, i.e. GCF of 12 and 40.
⇒ Factors of 12 and 40:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
Therefore, the GCF of 12 and 40 is 4.
Example 2: The product of two numbers is 480. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 480
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 480/4
Therefore, the LCM is 120.
Example 3: Find the GCF of 12 and 40, if their LCM is 120.

Solution:

∵ LCM × GCF = 12 × 40
⇒ GCF(12, 40) = (12 × 40)/120 = 4
Therefore, the greatest common factor of 12 and 40 is 4.

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FAQs on GCF of 12 and 40

What is the GCF of 12 and 40?

The GCF of 12 and 40 is 4. To calculate the greatest common factor of 12 and 40, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the greatest factor that exactly divides both 12 and 40, i.e., 4.

What is the Relation Between LCM and GCF of 12, 40?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 12 and 40, i.e. GCF × LCM = 12 × 40.

If the GCF of 40 and 12 is 4, Find its LCM.

GCF(40, 12) × LCM(40, 12) = 40 × 12
Since the GCF of 40 and 12 = 4
⇒ 4 × LCM(40, 12) = 480
Therefore, LCM = 120
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What are the Methods to Find GCF of 12 and 40?

There are three commonly used methods to find the GCF of 12 and 40.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the GCF of 12 and 40 by Long Division Method?

To find the GCF of 12, 40 using long division method, 40 is divided by 12. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

How to Find the GCF of 12 and 40 by Prime Factorization?

To find the GCF of 12 and 40, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 40 = 2 × 2 × 2 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 12 and 40. Hence, GCF(12, 40) = 2 × 2 = 4
☛ What are Prime Numbers?

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