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GCF of 18 and 72

GCF of 18 and 72 is the largest possible number that divides 18 and 72 exactly without any remainder. The factors of 18 and 72 are 1, 2, 3, 6, 9, 18 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 18 and 72 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 18 and 72
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 18 and 72?

Answer: GCF of 18 and 72 is 18.

Explanation:

The GCF of two non-zero integers, x(18) and y(72), is the greatest positive integer m(18) that divides both x(18) and y(72) without any remainder.

Methods to Find GCF of 18 and 72

The methods to find the GCF of 18 and 72 are explained below.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

GCF of 18 and 72 by Prime Factorization

Prime factorization of 18 and 72 is (2 × 3 × 3) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 18 and 72 have common prime factors. Hence, the GCF of 18 and 72 is 2 × 3 × 3 = 18.

GCF of 18 and 72 by Long Division

GCF of 18 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 18 (smaller number).
Step 2: Since the remainder = 0, the divisor (18) is the GCF of 18 and 72.

The corresponding divisor (18) is the GCF of 18 and 72.

GCF of 18 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 = 18

GCF(72, 18) = GCF(18, 72 mod 18) = GCF(18, 0)
GCF(18, 0) = 18 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 18 and 72 is 18.

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GCF of 18 and 72 Examples

Example 1: The product of two numbers is 1296. If their GCF is 18, what is their LCM?

Solution:

Given: GCF = 18 and product of numbers = 1296
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1296/18
Therefore, the LCM is 72.
Example 2: For two numbers, GCF = 18 and LCM = 72. If one number is 18, find the other number.

Solution:

Given: GCF (y, 18) = 18 and LCM (y, 18) = 72
∵ GCF × LCM = 18 × (y)
⇒ y = (GCF × LCM)/18
⇒ y = (18 × 72)/18
⇒ y = 72
Therefore, the other number is 72.
Example 3: Find the greatest number that divides 18 and 72 exactly.

Solution:

The greatest number that divides 18 and 72 exactly is their greatest common factor, i.e. GCF of 18 and 72.
⇒ Factors of 18 and 72:
- Factors of 18 = 1, 2, 3, 6, 9, 18
- Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Therefore, the GCF of 18 and 72 is 18.

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FAQs on GCF of 18 and 72

What is the GCF of 18 and 72?

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

How to Find the GCF of 18 and 72 by Long Division Method?

To find the GCF of 18, 72 using long division method, 72 is divided by 18. The corresponding divisor (18) when remainder equals 0 is taken as GCF.

If the GCF of 72 and 18 is 18, Find its LCM.

GCF(72, 18) × LCM(72, 18) = 72 × 18
Since the GCF of 72 and 18 = 18
⇒ 18 × LCM(72, 18) = 1296
Therefore, LCM = 72
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What are the Methods to Find GCF of 18 and 72?

There are three commonly used methods to find the GCF of 18 and 72.

By Long Division
By Prime Factorization
By Euclidean Algorithm

What is the Relation Between LCM and GCF of 18, 72?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 18 and 72, i.e. GCF × LCM = 18 × 72.

How to Find the GCF of 18 and 72 by Prime Factorization?

To find the GCF of 18 and 72, we will find the prime factorization of the given numbers, i.e. 18 = 2 × 3 × 3; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 3, 3 are common terms in the prime factorization of 18 and 72. Hence, GCF(18, 72) = 2 × 3 × 3 = 18
☛ Prime Number

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