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GCF of 66 and 88

GCF of 66 and 88 is the largest possible number that divides 66 and 88 exactly without any remainder. The factors of 66 and 88 are 1, 2, 3, 6, 11, 22, 33, 66 and 1, 2, 4, 8, 11, 22, 44, 88 respectively. There are 3 commonly used methods to find the GCF of 66 and 88 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 66 and 88
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 66 and 88?

Answer: GCF of 66 and 88 is 22.

Explanation:

The GCF of two non-zero integers, x(66) and y(88), is the greatest positive integer m(22) that divides both x(66) and y(88) without any remainder.

Methods to Find GCF of 66 and 88

Let's look at the different methods for finding the GCF of 66 and 88.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 66 and 88 by Long Division

GCF of 66 and 88 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 88 (larger number) by 66 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (66) by the remainder (22).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (22) is the GCF of 66 and 88.

GCF of 66 and 88 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 = 88 and Y = 66

GCF(88, 66) = GCF(66, 88 mod 66) = GCF(66, 22)
GCF(66, 22) = GCF(22, 66 mod 22) = GCF(22, 0)
GCF(22, 0) = 22 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 66 and 88 is 22.

GCF of 66 and 88 by Listing Common Factors

Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88

There are 4 common factors of 66 and 88, that are 1, 2, 11, and 22. Therefore, the greatest common factor of 66 and 88 is 22.

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GCF of 66 and 88 Examples

Example 1: The product of two numbers is 5808. If their GCF is 22, what is their LCM?

Solution:

Given: GCF = 22 and product of numbers = 5808
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 5808/22
Therefore, the LCM is 264.
Example 2: Find the GCF of 66 and 88, if their LCM is 264.

Solution:

∵ LCM × GCF = 66 × 88
⇒ GCF(66, 88) = (66 × 88)/264 = 22
Therefore, the greatest common factor of 66 and 88 is 22.
Example 3: For two numbers, GCF = 22 and LCM = 264. If one number is 88, find the other number.

Solution:

Given: GCF (x, 88) = 22 and LCM (x, 88) = 264
∵ GCF × LCM = 88 × (x)
⇒ x = (GCF × LCM)/88
⇒ x = (22 × 264)/88
⇒ x = 66
Therefore, the other number is 66.

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FAQs on GCF of 66 and 88

What is the GCF of 66 and 88?

The GCF of 66 and 88 is 22. To calculate the greatest common factor of 66 and 88, we need to factor each number (factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66; factors of 88 = 1, 2, 4, 8, 11, 22, 44, 88) and choose the greatest factor that exactly divides both 66 and 88, i.e., 22.

If the GCF of 88 and 66 is 22, Find its LCM.

GCF(88, 66) × LCM(88, 66) = 88 × 66
Since the GCF of 88 and 66 = 22
⇒ 22 × LCM(88, 66) = 5808
Therefore, LCM = 264
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 66, 88?

The following equation can be used to express the relation between Least Common Multiple and GCF of 66 and 88, i.e. GCF × LCM = 66 × 88.

What are the Methods to Find GCF of 66 and 88?

There are three commonly used methods to find the GCF of 66 and 88.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the GCF of 66 and 88 by Long Division Method?

To find the GCF of 66, 88 using long division method, 88 is divided by 66. The corresponding divisor (22) when remainder equals 0 is taken as GCF.

How to Find the GCF of 66 and 88 by Prime Factorization?

To find the GCF of 66 and 88, we will find the prime factorization of the given numbers, i.e. 66 = 2 × 3 × 11; 88 = 2 × 2 × 2 × 11.
⇒ Since 2, 11 are common terms in the prime factorization of 66 and 88. Hence, GCF(66, 88) = 2 × 11 = 22
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