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GCF of 36 and 40

GCF of 36 and 40 is the largest possible number that divides 36 and 40 exactly without any remainder. The factors of 36 and 40 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 4, 5, 8, 10, 20, 40 respectively. There are 3 commonly used methods to find the GCF of 36 and 40 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 36 and 40
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 36 and 40?

Answer: GCF of 36 and 40 is 4.

Explanation:

The GCF of two non-zero integers, x(36) and y(40), is the greatest positive integer m(4) that divides both x(36) and y(40) without any remainder.

Methods to Find GCF of 36 and 40

The methods to find the GCF of 36 and 40 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 36 and 40 by Long Division

GCF of 36 and 40 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 40 (larger number) by 36 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 36 and 40.

GCF of 36 and 40 by Prime Factorization

Prime factorization of 36 and 40 is (2 × 2 × 3 × 3) and (2 × 2 × 2 × 5) respectively. As visible, 36 and 40 have common prime factors. Hence, the GCF of 36 and 40 is 2 × 2 = 4.

GCF of 36 and 40 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 = 40 and Y = 36

GCF(40, 36) = GCF(36, 40 mod 36) = GCF(36, 4)
GCF(36, 4) = GCF(4, 36 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 36 and 40 is 4.

☛ Also Check:

GCF of 36 and 40 Examples

Example 1: Find the GCF of 36 and 40, if their LCM is 360.

Solution:

∵ LCM × GCF = 36 × 40
⇒ GCF(36, 40) = (36 × 40)/360 = 4
Therefore, the greatest common factor of 36 and 40 is 4.
Example 2: For two numbers, GCF = 4 and LCM = 360. If one number is 40, find the other number.

Solution:

Given: GCF (x, 40) = 4 and LCM (x, 40) = 360
∵ GCF × LCM = 40 × (x)
⇒ x = (GCF × LCM)/40
⇒ x = (4 × 360)/40
⇒ x = 36
Therefore, the other number is 36.
Example 3: Find the greatest number that divides 36 and 40 exactly.

Solution:

The greatest number that divides 36 and 40 exactly is their greatest common factor, i.e. GCF of 36 and 40.
⇒ Factors of 36 and 40:
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
Therefore, the GCF of 36 and 40 is 4.

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FAQs on GCF of 36 and 40

What is the GCF of 36 and 40?

The GCF of 36 and 40 is 4. To calculate the greatest common factor of 36 and 40, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the greatest factor that exactly divides both 36 and 40, i.e., 4.

How to Find the GCF of 36 and 40 by Prime Factorization?

To find the GCF of 36 and 40, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 40 = 2 × 2 × 2 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 36 and 40. Hence, GCF(36, 40) = 2 × 2 = 4
☛ Prime Number

If the GCF of 40 and 36 is 4, Find its LCM.

GCF(40, 36) × LCM(40, 36) = 40 × 36
Since the GCF of 40 and 36 = 4
⇒ 4 × LCM(40, 36) = 1440
Therefore, LCM = 360
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 36, 40?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 36 and 40, i.e. GCF × LCM = 36 × 40.

What are the Methods to Find GCF of 36 and 40?

There are three commonly used methods to find the GCF of 36 and 40.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the GCF of 36 and 40 by Long Division Method?

To find the GCF of 36, 40 using long division method, 40 is divided by 36. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

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