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GCF of 30 and 72

GCF of 30 and 72 is the largest possible number that divides 30 and 72 exactly without any remainder. The factors of 30 and 72 are 1, 2, 3, 5, 6, 10, 15, 30 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 30 and 72 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 30 and 72
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 30 and 72?

Answer: GCF of 30 and 72 is 6.

Explanation:

The GCF of two non-zero integers, x(30) and y(72), is the greatest positive integer m(6) that divides both x(30) and y(72) without any remainder.

Methods to Find GCF of 30 and 72

The methods to find the GCF of 30 and 72 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 30 and 72 by Listing Common Factors

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

There are 4 common factors of 30 and 72, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 30 and 72 is 6.

GCF of 30 and 72 by Prime Factorization

Prime factorization of 30 and 72 is (2 × 3 × 5) and (2 × 2 × 2 × 3 × 3) respectively. As visible, 30 and 72 have common prime factors. Hence, the GCF of 30 and 72 is 2 × 3 = 6.

GCF of 30 and 72 by Long Division

GCF of 30 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 30 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (30) by the remainder (12).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the GCF of 30 and 72.

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GCF of 30 and 72 Examples

Example 1: Find the GCF of 30 and 72, if their LCM is 360.

Solution:

∵ LCM × GCF = 30 × 72
⇒ GCF(30, 72) = (30 × 72)/360 = 6
Therefore, the greatest common factor of 30 and 72 is 6.
Example 2: Find the greatest number that divides 30 and 72 exactly.

Solution:

The greatest number that divides 30 and 72 exactly is their greatest common factor, i.e. GCF of 30 and 72.
⇒ Factors of 30 and 72:
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Therefore, the GCF of 30 and 72 is 6.
Example 3: For two numbers, GCF = 6 and LCM = 360. If one number is 30, find the other number.

Solution:

Given: GCF (x, 30) = 6 and LCM (x, 30) = 360
∵ GCF × LCM = 30 × (x)
⇒ x = (GCF × LCM)/30
⇒ x = (6 × 360)/30
⇒ x = 72
Therefore, the other number is 72.

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FAQs on GCF of 30 and 72

What is the GCF of 30 and 72?

The GCF of 30 and 72 is 6. To calculate the GCF (Greatest Common Factor) of 30 and 72, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72) and choose the greatest factor that exactly divides both 30 and 72, i.e., 6.

How to Find the GCF of 30 and 72 by Prime Factorization?

To find the GCF of 30 and 72, we will find the prime factorization of the given numbers, i.e. 30 = 2 × 3 × 5; 72 = 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 3 are common terms in the prime factorization of 30 and 72. Hence, GCF(30, 72) = 2 × 3 = 6
☛ What is a Prime Number?

What are the Methods to Find GCF of 30 and 72?

There are three commonly used methods to find the GCF of 30 and 72.

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the GCF of 30 and 72 by Long Division Method?

To find the GCF of 30, 72 using long division method, 72 is divided by 30. The corresponding divisor (6) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 30, 72?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 30 and 72, i.e. GCF × LCM = 30 × 72.

If the GCF of 72 and 30 is 6, Find its LCM.

GCF(72, 30) × LCM(72, 30) = 72 × 30
Since the GCF of 72 and 30 = 6
⇒ 6 × LCM(72, 30) = 2160
Therefore, LCM = 360
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