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GCF of 36 and 99

GCF of 36 and 99 is the largest possible number that divides 36 and 99 exactly without any remainder. The factors of 36 and 99 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 3, 9, 11, 33, 99 respectively. There are 3 commonly used methods to find the GCF of 36 and 99 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 36 and 99
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 36 and 99?

Answer: GCF of 36 and 99 is 9.

Explanation:

The GCF of two non-zero integers, x(36) and y(99), is the greatest positive integer m(9) that divides both x(36) and y(99) without any remainder.

Methods to Find GCF of 36 and 99

Let's look at the different methods for finding the GCF of 36 and 99.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

GCF of 36 and 99 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 99: 1, 3, 9, 11, 33, 99

There are 3 common factors of 36 and 99, that are 1, 3, and 9. Therefore, the greatest common factor of 36 and 99 is 9.

GCF of 36 and 99 by Prime Factorization

Prime factorization of 36 and 99 is (2 × 2 × 3 × 3) and (3 × 3 × 11) respectively. As visible, 36 and 99 have common prime factors. Hence, the GCF of 36 and 99 is 3 × 3 = 9.

GCF of 36 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 = 36

GCF(99, 36) = GCF(36, 99 mod 36) = GCF(36, 27)
GCF(36, 27) = GCF(27, 36 mod 27) = GCF(27, 9)
GCF(27, 9) = GCF(9, 27 mod 9) = GCF(9, 0)
GCF(9, 0) = 9 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 36 and 99 is 9.

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GCF of 36 and 99 Examples

Example 1: The product of two numbers is 3564. If their GCF is 9, what is their LCM?

Solution:

Given: GCF = 9 and product of numbers = 3564
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 3564/9
Therefore, the LCM is 396.
Example 2: Find the GCF of 36 and 99, if their LCM is 396.

Solution:

∵ LCM × GCF = 36 × 99
⇒ GCF(36, 99) = (36 × 99)/396 = 9
Therefore, the greatest common factor of 36 and 99 is 9.
Example 3: For two numbers, GCF = 9 and LCM = 396. If one number is 99, find the other number.

Solution:

Given: GCF (y, 99) = 9 and LCM (y, 99) = 396
∵ GCF × LCM = 99 × (y)
⇒ y = (GCF × LCM)/99
⇒ y = (9 × 396)/99
⇒ y = 36
Therefore, the other number is 36.

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FAQs on GCF of 36 and 99

What is the GCF of 36 and 99?

The GCF of 36 and 99 is 9. To calculate the GCF (Greatest Common Factor) of 36 and 99, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 99 = 1, 3, 9, 11, 33, 99) and choose the greatest factor that exactly divides both 36 and 99, i.e., 9.

What are the Methods to Find GCF of 36 and 99?

There are three commonly used methods to find the GCF of 36 and 99.

By Prime Factorization
By Listing Common Factors
By Long Division

If the GCF of 99 and 36 is 9, Find its LCM.

GCF(99, 36) × LCM(99, 36) = 99 × 36
Since the GCF of 99 and 36 = 9
⇒ 9 × LCM(99, 36) = 3564
Therefore, LCM = 396
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What is the Relation Between LCM and GCF of 36, 99?

The following equation can be used to express the relation between LCM and GCF of 36 and 99, i.e. GCF × LCM = 36 × 99.

How to Find the GCF of 36 and 99 by Long Division Method?

To find the GCF of 36, 99 using long division method, 99 is divided by 36. The corresponding divisor (9) when remainder equals 0 is taken as GCF.

How to Find the GCF of 36 and 99 by Prime Factorization?

To find the GCF of 36 and 99, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 99 = 3 × 3 × 11.
⇒ Since 3, 3 are common terms in the prime factorization of 36 and 99. Hence, GCF(36, 99) = 3 × 3 = 9
☛ What are Prime Numbers?

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