A day full of math games & activities. Find one near you.

GCF of 36 and 100

GCF of 36 and 100 is the largest possible number that divides 36 and 100 exactly without any remainder. The factors of 36 and 100 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and 1, 2, 4, 5, 10, 20, 25, 50, 100 respectively. There are 3 commonly used methods to find the GCF of 36 and 100 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 36 and 100
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 36 and 100?

Answer: GCF of 36 and 100 is 4.

Explanation:

The GCF of two non-zero integers, x(36) and y(100), is the greatest positive integer m(4) that divides both x(36) and y(100) without any remainder.

Methods to Find GCF of 36 and 100

Let's look at the different methods for finding the GCF of 36 and 100.

Listing Common Factors
Long Division Method
Using Euclid's Algorithm

GCF of 36 and 100 by Listing Common Factors

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

There are 3 common factors of 36 and 100, that are 1, 2, and 4. Therefore, the greatest common factor of 36 and 100 is 4.

GCF of 36 and 100 by Long Division

GCF of 36 and 100 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 100 (larger number) by 36 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (36) by the remainder (28).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 36 and 100.

GCF of 36 and 100 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 = 100 and Y = 36

GCF(100, 36) = GCF(36, 100 mod 36) = GCF(36, 28)
GCF(36, 28) = GCF(28, 36 mod 28) = GCF(28, 8)
GCF(28, 8) = GCF(8, 28 mod 8) = GCF(8, 4)
GCF(8, 4) = GCF(4, 8 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 36 and 100 is 4.

☛ Also Check:

GCF of 36 and 100 Examples

Example 1: For two numbers, GCF = 4 and LCM = 900. If one number is 100, find the other number.

Solution:

Given: GCF (z, 100) = 4 and LCM (z, 100) = 900
∵ GCF × LCM = 100 × (z)
⇒ z = (GCF × LCM)/100
⇒ z = (4 × 900)/100
⇒ z = 36
Therefore, the other number is 36.
Example 2: Find the greatest number that divides 36 and 100 exactly.

Solution:

The greatest number that divides 36 and 100 exactly is their greatest common factor, i.e. GCF of 36 and 100.
⇒ Factors of 36 and 100:
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
- Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
Therefore, the GCF of 36 and 100 is 4.
Example 3: Find the GCF of 36 and 100, if their LCM is 900.

Solution:

∵ LCM × GCF = 36 × 100
⇒ GCF(36, 100) = (36 × 100)/900 = 4
Therefore, the greatest common factor of 36 and 100 is 4.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 36 and 100

What is the GCF of 36 and 100?

The GCF of 36 and 100 is 4. To calculate the GCF (Greatest Common Factor) of 36 and 100, we need to factor each number (factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36; factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100) and choose the greatest factor that exactly divides both 36 and 100, i.e., 4.

How to Find the GCF of 36 and 100 by Long Division Method?

To find the GCF of 36, 100 using long division method, 100 is divided by 36. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 36, 100?

The following equation can be used to express the relation between LCM and GCF of 36 and 100, i.e. GCF × LCM = 36 × 100.

If the GCF of 100 and 36 is 4, Find its LCM.

GCF(100, 36) × LCM(100, 36) = 100 × 36
Since the GCF of 100 and 36 = 4
⇒ 4 × LCM(100, 36) = 3600
Therefore, LCM = 900
☛ GCF Calculator

How to Find the GCF of 36 and 100 by Prime Factorization?

To find the GCF of 36 and 100, we will find the prime factorization of the given numbers, i.e. 36 = 2 × 2 × 3 × 3; 100 = 2 × 2 × 5 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 36 and 100. Hence, GCF(36, 100) = 2 × 2 = 4
☛ What are Prime Numbers?

What are the Methods to Find GCF of 36 and 100?

There are three commonly used methods to find the GCF of 36 and 100.

By Listing Common Factors
By Long Division
By Prime Factorization

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum