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GCF of 27 and 72

GCF of 27 and 72 is the largest possible number that divides 27 and 72 exactly without any remainder. The factors of 27 and 72 are 1, 3, 9, 27 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 27 and 72 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 27 and 72
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 27 and 72?

Answer: GCF of 27 and 72 is 9.

Explanation:

The GCF of two non-zero integers, x(27) and y(72), is the greatest positive integer m(9) that divides both x(27) and y(72) without any remainder.

Methods to Find GCF of 27 and 72

Let's look at the different methods for finding the GCF of 27 and 72.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 27 and 72 by Long Division

GCF of 27 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 27 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (27) by the remainder (18).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (9) is the GCF of 27 and 72.

GCF of 27 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 = 27

GCF(72, 27) = GCF(27, 72 mod 27) = GCF(27, 18)
GCF(27, 18) = GCF(18, 27 mod 18) = GCF(18, 9)
GCF(18, 9) = GCF(9, 18 mod 9) = GCF(9, 0)
GCF(9, 0) = 9 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 27 and 72 is 9.

GCF of 27 and 72 by Listing Common Factors

Factors of 27: 1, 3, 9, 27
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

There are 3 common factors of 27 and 72, that are 1, 3, and 9. Therefore, the greatest common factor of 27 and 72 is 9.

☛ Also Check:

GCF of 27 and 72 Examples

Example 1: The product of two numbers is 1944. If their GCF is 9, what is their LCM?

Solution:

Given: GCF = 9 and product of numbers = 1944
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1944/9
Therefore, the LCM is 216.
Example 2: Find the GCF of 27 and 72, if their LCM is 216.

Solution:

∵ LCM × GCF = 27 × 72
⇒ GCF(27, 72) = (27 × 72)/216 = 9
Therefore, the greatest common factor of 27 and 72 is 9.
Example 3: Find the greatest number that divides 27 and 72 exactly.

Solution:

The greatest number that divides 27 and 72 exactly is their greatest common factor, i.e. GCF of 27 and 72.
⇒ Factors of 27 and 72:
- Factors of 27 = 1, 3, 9, 27
- Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Therefore, the GCF of 27 and 72 is 9.

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FAQs on GCF of 27 and 72

What is the GCF of 27 and 72?

The GCF of 27 and 72 is 9. To calculate the GCF of 27 and 72, we need to factor each number (factors of 27 = 1, 3, 9, 27; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the greatest factor that exactly divides both 27 and 72, i.e., 9.

If the GCF of 72 and 27 is 9, Find its LCM.

GCF(72, 27) × LCM(72, 27) = 72 × 27
Since the GCF of 72 and 27 = 9
⇒ 9 × LCM(72, 27) = 1944
Therefore, LCM = 216
☛ GCF Calculator

What are the Methods to Find GCF of 27 and 72?

There are three commonly used methods to find the GCF of 27 and 72.

By Listing Common Factors
By Prime Factorization
By Long Division

How to Find the GCF of 27 and 72 by Prime Factorization?

To find the GCF of 27 and 72, we will find the prime factorization of the given numbers, i.e. 27 = 3 × 3 × 3; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 3, 3 are common terms in the prime factorization of 27 and 72. Hence, GCF(27, 72) = 3 × 3 = 9
☛ Prime Numbers

What is the Relation Between LCM and GCF of 27, 72?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 27 and 72, i.e. GCF × LCM = 27 × 72.

How to Find the GCF of 27 and 72 by Long Division Method?

To find the GCF of 27, 72 using long division method, 72 is divided by 27. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

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