A day full of math games & activities. Find one near you.

GCF of 66 and 99

GCF of 66 and 99 is the largest possible number that divides 66 and 99 exactly without any remainder. The factors of 66 and 99 are 1, 2, 3, 6, 11, 22, 33, 66 and 1, 3, 9, 11, 33, 99 respectively. There are 3 commonly used methods to find the GCF of 66 and 99 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 66 and 99
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 66 and 99?

Answer: GCF of 66 and 99 is 33.

Explanation:

The GCF of two non-zero integers, x(66) and y(99), is the greatest positive integer m(33) that divides both x(66) and y(99) without any remainder.

Methods to Find GCF of 66 and 99

The methods to find the GCF of 66 and 99 are explained below.

Prime Factorization Method
Using Euclid's Algorithm
Long Division Method

GCF of 66 and 99 by Prime Factorization

Prime factorization of 66 and 99 is (2 × 3 × 11) and (3 × 3 × 11) respectively. As visible, 66 and 99 have common prime factors. Hence, the GCF of 66 and 99 is 3 × 11 = 33.

GCF of 66 and 99 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 = 99 and Y = 66

GCF(99, 66) = GCF(66, 99 mod 66) = GCF(66, 33)
GCF(66, 33) = GCF(33, 66 mod 33) = GCF(33, 0)
GCF(33, 0) = 33 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 66 and 99 is 33.

GCF of 66 and 99 by Long Division

GCF of 66 and 99 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 99 (larger number) by 66 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (66) by the remainder (33).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (33) is the GCF of 66 and 99.

☛ Also Check:

GCF of 66 and 99 Examples

Example 1: Find the GCF of 66 and 99, if their LCM is 198.

Solution:

∵ LCM × GCF = 66 × 99
⇒ GCF(66, 99) = (66 × 99)/198 = 33
Therefore, the greatest common factor of 66 and 99 is 33.
Example 2: The product of two numbers is 6534. If their GCF is 33, what is their LCM?

Solution:

Given: GCF = 33 and product of numbers = 6534
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 6534/33
Therefore, the LCM is 198.
Example 3: Find the greatest number that divides 66 and 99 exactly.

Solution:

The greatest number that divides 66 and 99 exactly is their greatest common factor, i.e. GCF of 66 and 99.
⇒ Factors of 66 and 99:
- Factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66
- Factors of 99 = 1, 3, 9, 11, 33, 99
Therefore, the GCF of 66 and 99 is 33.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 66 and 99

What is the GCF of 66 and 99?

The GCF of 66 and 99 is 33. To calculate the GCF of 66 and 99, we need to factor each number (factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66; factors of 99 = 1, 3, 9, 11, 33, 99) and choose the greatest factor that exactly divides both 66 and 99, i.e., 33.

What is the Relation Between LCM and GCF of 66, 99?

The following equation can be used to express the relation between Least Common Multiple and GCF of 66 and 99, i.e. GCF × LCM = 66 × 99.

If the GCF of 99 and 66 is 33, Find its LCM.

GCF(99, 66) × LCM(99, 66) = 99 × 66
Since the GCF of 99 and 66 = 33
⇒ 33 × LCM(99, 66) = 6534
Therefore, LCM = 198
☛ Greatest Common Factor Calculator

How to Find the GCF of 66 and 99 by Long Division Method?

To find the GCF of 66, 99 using long division method, 99 is divided by 66. The corresponding divisor (33) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 66 and 99?

There are three commonly used methods to find the GCF of 66 and 99.

By Euclidean Algorithm
By Long Division
By Prime Factorization

How to Find the GCF of 66 and 99 by Prime Factorization?

To find the GCF of 66 and 99, we will find the prime factorization of the given numbers, i.e. 66 = 2 × 3 × 11; 99 = 3 × 3 × 11.
⇒ Since 3, 11 are common terms in the prime factorization of 66 and 99. Hence, GCF(66, 99) = 3 × 11 = 33
☛ Prime Numbers

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum