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GCF of 30 and 66

GCF of 30 and 66 is the largest possible number that divides 30 and 66 exactly without any remainder. The factors of 30 and 66 are 1, 2, 3, 5, 6, 10, 15, 30 and 1, 2, 3, 6, 11, 22, 33, 66 respectively. There are 3 commonly used methods to find the GCF of 30 and 66 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 30 and 66
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 30 and 66?

Answer: GCF of 30 and 66 is 6.

Explanation:

The GCF of two non-zero integers, x(30) and y(66), is the greatest positive integer m(6) that divides both x(30) and y(66) without any remainder.

Methods to Find GCF of 30 and 66

Let's look at the different methods for finding the GCF of 30 and 66.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 30 and 66 by Long Division

GCF of 30 and 66 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 66 (larger number) by 30 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (30) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the GCF of 30 and 66.

GCF of 30 and 66 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 = 66 and Y = 30

GCF(66, 30) = GCF(30, 66 mod 30) = GCF(30, 6)
GCF(30, 6) = GCF(6, 30 mod 6) = GCF(6, 0)
GCF(6, 0) = 6 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 30 and 66 is 6.

GCF of 30 and 66 by Listing Common Factors

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66

There are 4 common factors of 30 and 66, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 30 and 66 is 6.

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GCF of 30 and 66 Examples

Example 1: Find the GCF of 30 and 66, if their LCM is 330.

Solution:

∵ LCM × GCF = 30 × 66
⇒ GCF(30, 66) = (30 × 66)/330 = 6
Therefore, the greatest common factor of 30 and 66 is 6.
Example 2: The product of two numbers is 1980. If their GCF is 6, what is their LCM?

Solution:

Given: GCF = 6 and product of numbers = 1980
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1980/6
Therefore, the LCM is 330.
Example 3: For two numbers, GCF = 6 and LCM = 330. If one number is 66, find the other number.

Solution:

Given: GCF (y, 66) = 6 and LCM (y, 66) = 330
∵ GCF × LCM = 66 × (y)
⇒ y = (GCF × LCM)/66
⇒ y = (6 × 330)/66
⇒ y = 30
Therefore, the other number is 30.

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FAQs on GCF of 30 and 66

What is the GCF of 30 and 66?

The GCF of 30 and 66 is 6. To calculate the GCF of 30 and 66, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66) and choose the greatest factor that exactly divides both 30 and 66, i.e., 6.

How to Find the GCF of 30 and 66 by Long Division Method?

To find the GCF of 30, 66 using long division method, 66 is divided by 30. The corresponding divisor (6) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 30 and 66?

There are three commonly used methods to find the GCF of 30 and 66.

By Prime Factorization
By Long Division
By Listing Common Factors

If the GCF of 66 and 30 is 6, Find its LCM.

GCF(66, 30) × LCM(66, 30) = 66 × 30
Since the GCF of 66 and 30 = 6
⇒ 6 × LCM(66, 30) = 1980
Therefore, LCM = 330
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What is the Relation Between LCM and GCF of 30, 66?

The following equation can be used to express the relation between LCM and GCF of 30 and 66, i.e. GCF × LCM = 30 × 66.

How to Find the GCF of 30 and 66 by Prime Factorization?

To find the GCF of 30 and 66, we will find the prime factorization of the given numbers, i.e. 30 = 2 × 3 × 5; 66 = 2 × 3 × 11.
⇒ Since 2, 3 are common terms in the prime factorization of 30 and 66. Hence, GCF(30, 66) = 2 × 3 = 6
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