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GCF of 66 and 90

GCF of 66 and 90 is the largest possible number that divides 66 and 90 exactly without any remainder. The factors of 66 and 90 are 1, 2, 3, 6, 11, 22, 33, 66 and 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 respectively. There are 3 commonly used methods to find the GCF of 66 and 90 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 66 and 90
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 66 and 90?

Answer: GCF of 66 and 90 is 6.

Explanation:

The GCF of two non-zero integers, x(66) and y(90), is the greatest positive integer m(6) that divides both x(66) and y(90) without any remainder.

Methods to Find GCF of 66 and 90

The methods to find the GCF of 66 and 90 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 66 and 90 by Listing Common Factors

Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

There are 4 common factors of 66 and 90, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 66 and 90 is 6.

GCF of 66 and 90 by Long Division

GCF of 66 and 90 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 90 (larger number) by 66 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (66) by the remainder (24).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the GCF of 66 and 90.

GCF of 66 and 90 by Prime Factorization

Prime factorization of 66 and 90 is (2 × 3 × 11) and (2 × 3 × 3 × 5) respectively. As visible, 66 and 90 have common prime factors. Hence, the GCF of 66 and 90 is 2 × 3 = 6.

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GCF of 66 and 90 Examples

Example 1: The product of two numbers is 5940. If their GCF is 6, what is their LCM?

Solution:

Given: GCF = 6 and product of numbers = 5940
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 5940/6
Therefore, the LCM is 990.
Example 2: For two numbers, GCF = 6 and LCM = 990. If one number is 66, find the other number.

Solution:

Given: GCF (y, 66) = 6 and LCM (y, 66) = 990
∵ GCF × LCM = 66 × (y)
⇒ y = (GCF × LCM)/66
⇒ y = (6 × 990)/66
⇒ y = 90
Therefore, the other number is 90.
Example 3: Find the GCF of 66 and 90, if their LCM is 990.

Solution:

∵ LCM × GCF = 66 × 90
⇒ GCF(66, 90) = (66 × 90)/990 = 6
Therefore, the greatest common factor of 66 and 90 is 6.

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FAQs on GCF of 66 and 90

What is the GCF of 66 and 90?

The GCF of 66 and 90 is 6. To calculate the greatest common factor (GCF) of 66 and 90, we need to factor each number (factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66; factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90) and choose the greatest factor that exactly divides both 66 and 90, i.e., 6.

How to Find the GCF of 66 and 90 by Prime Factorization?

To find the GCF of 66 and 90, we will find the prime factorization of the given numbers, i.e. 66 = 2 × 3 × 11; 90 = 2 × 3 × 3 × 5.
⇒ Since 2, 3 are common terms in the prime factorization of 66 and 90. Hence, GCF(66, 90) = 2 × 3 = 6
☛ Prime Number

How to Find the GCF of 66 and 90 by Long Division Method?

To find the GCF of 66, 90 using long division method, 90 is divided by 66. The corresponding divisor (6) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 66, 90?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 66 and 90, i.e. GCF × LCM = 66 × 90.

What are the Methods to Find GCF of 66 and 90?

There are three commonly used methods to find the GCF of 66 and 90.

By Prime Factorization
By Long Division
By Euclidean Algorithm

If the GCF of 90 and 66 is 6, Find its LCM.

GCF(90, 66) × LCM(90, 66) = 90 × 66
Since the GCF of 90 and 66 = 6
⇒ 6 × LCM(90, 66) = 5940
Therefore, LCM = 990
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