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

GCF of 55 and 66

GCF of 55 and 66 is the largest possible number that divides 55 and 66 exactly without any remainder. The factors of 55 and 66 are 1, 5, 11, 55 and 1, 2, 3, 6, 11, 22, 33, 66 respectively. There are 3 commonly used methods to find the GCF of 55 and 66 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 55 and 66
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 55 and 66?

Answer: GCF of 55 and 66 is 11.

Explanation:

The GCF of two non-zero integers, x(55) and y(66), is the greatest positive integer m(11) that divides both x(55) and y(66) without any remainder.

Methods to Find GCF of 55 and 66

Let's look at the different methods for finding the GCF of 55 and 66.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 55 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 = 55

GCF(66, 55) = GCF(55, 66 mod 55) = GCF(55, 11)
GCF(55, 11) = GCF(11, 55 mod 11) = GCF(11, 0)
GCF(11, 0) = 11 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 55 and 66 is 11.

GCF of 55 and 66 by Long Division

GCF of 55 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 55 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (55) by the remainder (11).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (11) is the GCF of 55 and 66.

GCF of 55 and 66 by Prime Factorization

Prime factorization of 55 and 66 is (5 × 11) and (2 × 3 × 11) respectively. As visible, 55 and 66 have only one common prime factor i.e. 11. Hence, the GCF of 55 and 66 is 11.

☛ Also Check:

GCF of 55 and 66 Examples

Example 1: For two numbers, GCF = 11 and LCM = 330. If one number is 66, find the other number.

Solution:

Given: GCF (x, 66) = 11 and LCM (x, 66) = 330
∵ GCF × LCM = 66 × (x)
⇒ x = (GCF × LCM)/66
⇒ x = (11 × 330)/66
⇒ x = 55
Therefore, the other number is 55.
Example 2: Find the GCF of 55 and 66, if their LCM is 330.

Solution:

∵ LCM × GCF = 55 × 66
⇒ GCF(55, 66) = (55 × 66)/330 = 11
Therefore, the greatest common factor of 55 and 66 is 11.
Example 3: Find the greatest number that divides 55 and 66 exactly.

Solution:

The greatest number that divides 55 and 66 exactly is their greatest common factor, i.e. GCF of 55 and 66.
⇒ Factors of 55 and 66:
- Factors of 55 = 1, 5, 11, 55
- Factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66
Therefore, the GCF of 55 and 66 is 11.

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 55 and 66

What is the GCF of 55 and 66?

The GCF of 55 and 66 is 11. To calculate the greatest common factor of 55 and 66, we need to factor each number (factors of 55 = 1, 5, 11, 55; factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66) and choose the greatest factor that exactly divides both 55 and 66, i.e., 11.

How to Find the GCF of 55 and 66 by Prime Factorization?

To find the GCF of 55 and 66, we will find the prime factorization of the given numbers, i.e. 55 = 5 × 11; 66 = 2 × 3 × 11.
⇒ Since 11 is the only common prime factor of 55 and 66. Hence, GCF (55, 66) = 11.
☛ Prime Number

If the GCF of 66 and 55 is 11, Find its LCM.

GCF(66, 55) × LCM(66, 55) = 66 × 55
Since the GCF of 66 and 55 = 11
⇒ 11 × LCM(66, 55) = 3630
Therefore, LCM = 330
☛ GCF Calculator

What are the Methods to Find GCF of 55 and 66?

There are three commonly used methods to find the GCF of 55 and 66.

By Listing Common Factors
By Long Division
By Prime Factorization

How to Find the GCF of 55 and 66 by Long Division Method?

To find the GCF of 55, 66 using long division method, 66 is divided by 55. The corresponding divisor (11) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 55, 66?

The following equation can be used to express the relation between LCM and GCF of 55 and 66, i.e. GCF × LCM = 55 × 66.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum