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GCF of 12 and 72

GCF of 12 and 72 is the largest possible number that divides 12 and 72 exactly without any remainder. The factors of 12 and 72 are 1, 2, 3, 4, 6, 12 and 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 respectively. There are 3 commonly used methods to find the GCF of 12 and 72 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 12 and 72
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 72?

Answer: GCF of 12 and 72 is 12.

Explanation:

The GCF of two non-zero integers, x(12) and y(72), is the greatest positive integer m(12) that divides both x(12) and y(72) without any remainder.

Methods to Find GCF of 12 and 72

The methods to find the GCF of 12 and 72 are explained below.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

GCF of 12 and 72 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 = 72 and Y = 12

GCF(72, 12) = GCF(12, 72 mod 12) = GCF(12, 0)
GCF(12, 0) = 12 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 12 and 72 is 12.

GCF of 12 and 72 by Listing Common Factors

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

There are 6 common factors of 12 and 72, that are 1, 2, 3, 4, 6, and 12. Therefore, the greatest common factor of 12 and 72 is 12.

GCF of 12 and 72 by Long Division

GCF of 12 and 72 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 72 (larger number) by 12 (smaller number).
Step 2: Since the remainder = 0, the divisor (12) is the GCF of 12 and 72.

The corresponding divisor (12) is the GCF of 12 and 72.

☛ Also Check:

GCF of 12 and 72 Examples

Example 1: Find the GCF of 12 and 72, if their LCM is 72.

Solution:

∵ LCM × GCF = 12 × 72
⇒ GCF(12, 72) = (12 × 72)/72 = 12
Therefore, the greatest common factor of 12 and 72 is 12.
Example 2: The product of two numbers is 864. If their GCF is 12, what is their LCM?

Solution:

Given: GCF = 12 and product of numbers = 864
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 864/12
Therefore, the LCM is 72.
Example 3: For two numbers, GCF = 12 and LCM = 72. If one number is 12, find the other number.

Solution:

Given: GCF (z, 12) = 12 and LCM (z, 12) = 72
∵ GCF × LCM = 12 × (z)
⇒ z = (GCF × LCM)/12
⇒ z = (12 × 72)/12
⇒ z = 72
Therefore, the other number is 72.

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FAQs on GCF of 12 and 72

What is the GCF of 12 and 72?

The GCF of 12 and 72 is 12. To calculate the greatest common factor of 12 and 72, we need to factor each number (factors of 12 = 1, 2, 3, 4, 6, 12; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the greatest factor that exactly divides both 12 and 72, i.e., 12.

What is the Relation Between LCM and GCF of 12, 72?

The following equation can be used to express the relation between LCM and GCF of 12 and 72, i.e. GCF × LCM = 12 × 72.

How to Find the GCF of 12 and 72 by Long Division Method?

To find the GCF of 12, 72 using long division method, 72 is divided by 12. The corresponding divisor (12) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 12 and 72?

There are three commonly used methods to find the GCF of 12 and 72.

By Listing Common Factors
By Prime Factorization
By Long Division

How to Find the GCF of 12 and 72 by Prime Factorization?

To find the GCF of 12 and 72, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 3 are common terms in the prime factorization of 12 and 72. Hence, GCF(12, 72) = 2 × 2 × 3 = 12
☛ Prime Number

If the GCF of 72 and 12 is 12, Find its LCM.

GCF(72, 12) × LCM(72, 12) = 72 × 12
Since the GCF of 72 and 12 = 12
⇒ 12 × LCM(72, 12) = 864
Therefore, LCM = 72
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