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GCF of 33 and 66

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

1.	GCF of 33 and 66
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 33 and 66?

Answer: GCF of 33 and 66 is 33.

Explanation:

The GCF of two non-zero integers, x(33) and y(66), is the greatest positive integer m(33) that divides both x(33) and y(66) without any remainder.

Methods to Find GCF of 33 and 66

Let's look at the different methods for finding the GCF of 33 and 66.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 33 and 66 by Listing Common Factors

Factors of 33: 1, 3, 11, 33
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66

There are 4 common factors of 33 and 66, that are 3, 1, 11, and 33. Therefore, the greatest common factor of 33 and 66 is 33.

GCF of 33 and 66 by Prime Factorization

Prime factorization of 33 and 66 is (3 × 11) and (2 × 3 × 11) respectively. As visible, 33 and 66 have common prime factors. Hence, the GCF of 33 and 66 is 3 × 11 = 33.

GCF of 33 and 66 by Long Division

GCF of 33 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 33 (smaller number).
Step 2: Since the remainder = 0, the divisor (33) is the GCF of 33 and 66.

The corresponding divisor (33) is the GCF of 33 and 66.

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GCF of 33 and 66 Examples

Example 1: The product of two numbers is 2178. If their GCF is 33, what is their LCM?

Solution:

Given: GCF = 33 and product of numbers = 2178
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2178/33
Therefore, the LCM is 66.
Example 2: Find the greatest number that divides 33 and 66 exactly.

Solution:

The greatest number that divides 33 and 66 exactly is their greatest common factor, i.e. GCF of 33 and 66.
⇒ Factors of 33 and 66:
- Factors of 33 = 1, 3, 11, 33
- Factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66
Therefore, the GCF of 33 and 66 is 33.
Example 3: Find the GCF of 33 and 66, if their LCM is 66.

Solution:

∵ LCM × GCF = 33 × 66
⇒ GCF(33, 66) = (33 × 66)/66 = 33
Therefore, the greatest common factor of 33 and 66 is 33.

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FAQs on GCF of 33 and 66

What is the GCF of 33 and 66?

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

How to Find the GCF of 33 and 66 by Prime Factorization?

To find the GCF of 33 and 66, we will find the prime factorization of the given numbers, i.e. 33 = 3 × 11; 66 = 2 × 3 × 11.
⇒ Since 3, 11 are common terms in the prime factorization of 33 and 66. Hence, GCF(33, 66) = 3 × 11 = 33
☛ What is a Prime Number?

What is the Relation Between LCM and GCF of 33, 66?

The following equation can be used to express the relation between Least Common Multiple and GCF of 33 and 66, i.e. GCF × LCM = 33 × 66.

What are the Methods to Find GCF of 33 and 66?

There are three commonly used methods to find the GCF of 33 and 66.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the GCF of 33 and 66 by Long Division Method?

To find the GCF of 33, 66 using long division method, 66 is divided by 33. The corresponding divisor (33) when remainder equals 0 is taken as GCF.

If the GCF of 66 and 33 is 33, Find its LCM.

GCF(66, 33) × LCM(66, 33) = 66 × 33
Since the GCF of 66 and 33 = 33
⇒ 33 × LCM(66, 33) = 2178
Therefore, LCM = 66
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