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GCF of 50 and 72

GCF of 50 and 72 is the largest possible number that divides 50 and 72 exactly without any remainder. The factors of 50 and 72 are 1, 2, 5, 10, 25, 50 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 50 and 72 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 50 and 72
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 50 and 72?

Answer: GCF of 50 and 72 is 2.

Explanation:

The GCF of two non-zero integers, x(50) and y(72), is the greatest positive integer m(2) that divides both x(50) and y(72) without any remainder.

Methods to Find GCF of 50 and 72

Let's look at the different methods for finding the GCF of 50 and 72.

Prime Factorization Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 50 and 72 by Prime Factorization

Prime factorization of 50 and 72 is (2 × 5 × 5) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 50 and 72 have only one common prime factor i.e. 2. Hence, the GCF of 50 and 72 is 2.

GCF of 50 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 = 50

GCF(72, 50) = GCF(50, 72 mod 50) = GCF(50, 22)
GCF(50, 22) = GCF(22, 50 mod 22) = GCF(22, 6)
GCF(22, 6) = GCF(6, 22 mod 6) = GCF(6, 4)
GCF(6, 4) = GCF(4, 6 mod 4) = GCF(4, 2)
GCF(4, 2) = GCF(2, 4 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 50 and 72 is 2.

GCF of 50 and 72 by Listing Common Factors

Factors of 50: 1, 2, 5, 10, 25, 50
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

There are 2 common factors of 50 and 72, that are 1 and 2. Therefore, the greatest common factor of 50 and 72 is 2.

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GCF of 50 and 72 Examples

Example 1: Find the greatest number that divides 50 and 72 exactly.

Solution:

The greatest number that divides 50 and 72 exactly is their greatest common factor, i.e. GCF of 50 and 72.
⇒ Factors of 50 and 72:
- Factors of 50 = 1, 2, 5, 10, 25, 50
- Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Therefore, the GCF of 50 and 72 is 2.
Example 2: Find the GCF of 50 and 72, if their LCM is 1800.

Solution:

∵ LCM × GCF = 50 × 72
⇒ GCF(50, 72) = (50 × 72)/1800 = 2
Therefore, the greatest common factor of 50 and 72 is 2.
Example 3: For two numbers, GCF = 2 and LCM = 1800. If one number is 50, find the other number.

Solution:

Given: GCF (y, 50) = 2 and LCM (y, 50) = 1800
∵ GCF × LCM = 50 × (y)
⇒ y = (GCF × LCM)/50
⇒ y = (2 × 1800)/50
⇒ y = 72
Therefore, the other number is 72.

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FAQs on GCF of 50 and 72

What is the GCF of 50 and 72?

The GCF of 50 and 72 is 2. To calculate the greatest common factor (GCF) of 50 and 72, we need to factor each number (factors of 50 = 1, 2, 5, 10, 25, 50; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the greatest factor that exactly divides both 50 and 72, i.e., 2.

What is the Relation Between LCM and GCF of 50, 72?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 50 and 72, i.e. GCF × LCM = 50 × 72.

How to Find the GCF of 50 and 72 by Long Division Method?

To find the GCF of 50, 72 using long division method, 72 is divided by 50. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

If the GCF of 72 and 50 is 2, Find its LCM.

GCF(72, 50) × LCM(72, 50) = 72 × 50
Since the GCF of 72 and 50 = 2
⇒ 2 × LCM(72, 50) = 3600
Therefore, LCM = 1800
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What are the Methods to Find GCF of 50 and 72?

There are three commonly used methods to find the GCF of 50 and 72.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the GCF of 50 and 72 by Prime Factorization?

To find the GCF of 50 and 72, we will find the prime factorization of the given numbers, i.e. 50 = 2 × 5 × 5; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 2 is the only common prime factor of 50 and 72. Hence, GCF (50, 72) = 2.
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