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GCF of 36 and 144

GCF of 36 and 144 is the largest possible number that divides 36 and 144 exactly without any remainder. The factors of 36 and 144 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 respectively. There are 3 commonly used methods to find the GCF of 36 and 144 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 36 and 144
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 36 and 144?

Answer: GCF of 36 and 144 is 36.

Explanation:

The GCF of two non-zero integers, x(36) and y(144), is the greatest positive integer m(36) that divides both x(36) and y(144) without any remainder.

Methods to Find GCF of 36 and 144

The methods to find the GCF of 36 and 144 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 36 and 144 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 = 144 and Y = 36

GCF(144, 36) = GCF(36, 144 mod 36) = GCF(36, 0)
GCF(36, 0) = 36 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 36 and 144 is 36.

GCF of 36 and 144 by Long Division

GCF of 36 and 144 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 144 (larger number) by 36 (smaller number).
Step 2: Since the remainder = 0, the divisor (36) is the GCF of 36 and 144.

The corresponding divisor (36) is the GCF of 36 and 144.

GCF of 36 and 144 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144

There are 9 common factors of 36 and 144, that are 1, 2, 3, 4, 36, 6, 9, 12, and 18. Therefore, the greatest common factor of 36 and 144 is 36.

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GCF of 36 and 144 Examples

Example 1: The product of two numbers is 5184. If their GCF is 36, what is their LCM?

Solution:

Given: GCF = 36 and product of numbers = 5184
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 5184/36
Therefore, the LCM is 144.
Example 2: For two numbers, GCF = 36 and LCM = 144. If one number is 144, find the other number.

Solution:

Given: GCF (y, 144) = 36 and LCM (y, 144) = 144
∵ GCF × LCM = 144 × (y)
⇒ y = (GCF × LCM)/144
⇒ y = (36 × 144)/144
⇒ y = 36
Therefore, the other number is 36.
Example 3: Find the greatest number that divides 36 and 144 exactly.

Solution:

The greatest number that divides 36 and 144 exactly is their greatest common factor, i.e. GCF of 36 and 144.
⇒ Factors of 36 and 144:
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Therefore, the GCF of 36 and 144 is 36.

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FAQs on GCF of 36 and 144

What is the GCF of 36 and 144?

The GCF of 36 and 144 is 36. To calculate the GCF of 36 and 144, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144) and choose the greatest factor that exactly divides both 36 and 144, i.e., 36.

What are the Methods to Find GCF of 36 and 144?

There are three commonly used methods to find the GCF of 36 and 144.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the GCF of 36 and 144 by Long Division Method?

To find the GCF of 36, 144 using long division method, 144 is divided by 36. The corresponding divisor (36) when remainder equals 0 is taken as GCF.

If the GCF of 144 and 36 is 36, Find its LCM.

GCF(144, 36) × LCM(144, 36) = 144 × 36
Since the GCF of 144 and 36 = 36
⇒ 36 × LCM(144, 36) = 5184
Therefore, LCM = 144
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What is the Relation Between LCM and GCF of 36, 144?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 36 and 144, i.e. GCF × LCM = 36 × 144.

How to Find the GCF of 36 and 144 by Prime Factorization?

To find the GCF of 36 and 144, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 144 = 2 × 2 × 2 × 2 × 3 × 3.
⇒ Since 2, 2, 3, 3 are common terms in the prime factorization of 36 and 144. Hence, GCF(36, 144) = 2 × 2 × 3 × 3 = 36
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