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

GCF of 55 and 100

GCF of 55 and 100 is the largest possible number that divides 55 and 100 exactly without any remainder. The factors of 55 and 100 are 1, 5, 11, 55 and 1, 2, 4, 5, 10, 20, 25, 50, 100 respectively. There are 3 commonly used methods to find the GCF of 55 and 100 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 55 and 100
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 55 and 100?

Answer: GCF of 55 and 100 is 5.

Explanation:

The GCF of two non-zero integers, x(55) and y(100), is the greatest positive integer m(5) that divides both x(55) and y(100) without any remainder.

Methods to Find GCF of 55 and 100

Let's look at the different methods for finding the GCF of 55 and 100.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

GCF of 55 and 100 by Prime Factorization

Prime factorization of 55 and 100 is (5 × 11) and (2 × 2 × 5 × 5) respectively. As visible, 55 and 100 have only one common prime factor i.e. 5. Hence, the GCF of 55 and 100 is 5.

GCF of 55 and 100 by Long Division

GCF of 55 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 55 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (55) by the remainder (45).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 55 and 100.

GCF of 55 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 = 55

GCF(100, 55) = GCF(55, 100 mod 55) = GCF(55, 45)
GCF(55, 45) = GCF(45, 55 mod 45) = GCF(45, 10)
GCF(45, 10) = GCF(10, 45 mod 10) = GCF(10, 5)
GCF(10, 5) = GCF(5, 10 mod 5) = GCF(5, 0)
GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 55 and 100 is 5.

☛ Also Check:

GCF of 55 and 100 Examples

Example 1: Find the greatest number that divides 55 and 100 exactly.

Solution:

The greatest number that divides 55 and 100 exactly is their greatest common factor, i.e. GCF of 55 and 100.
⇒ Factors of 55 and 100:
- Factors of 55 = 1, 5, 11, 55
- Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
Therefore, the GCF of 55 and 100 is 5.
Example 2: Find the GCF of 55 and 100, if their LCM is 1100.

Solution:

∵ LCM × GCF = 55 × 100
⇒ GCF(55, 100) = (55 × 100)/1100 = 5
Therefore, the greatest common factor of 55 and 100 is 5.
Example 3: The product of two numbers is 5500. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 5500
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 5500/5
Therefore, the LCM is 1100.

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 55 and 100

What is the GCF of 55 and 100?

The GCF of 55 and 100 is 5. To calculate the GCF (Greatest Common Factor) of 55 and 100, we need to factor each number (factors of 55 = 1, 5, 11, 55; factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100) and choose the greatest factor that exactly divides both 55 and 100, i.e., 5.

If the GCF of 100 and 55 is 5, Find its LCM.

GCF(100, 55) × LCM(100, 55) = 100 × 55
Since the GCF of 100 and 55 = 5
⇒ 5 × LCM(100, 55) = 5500
Therefore, LCM = 1100
☛ GCF Calculator

How to Find the GCF of 55 and 100 by Long Division Method?

To find the GCF of 55, 100 using long division method, 100 is divided by 55. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

How to Find the GCF of 55 and 100 by Prime Factorization?

To find the GCF of 55 and 100, we will find the prime factorization of the given numbers, i.e. 55 = 5 × 11; 100 = 2 × 2 × 5 × 5.
⇒ Since 5 is the only common prime factor of 55 and 100. Hence, GCF (55, 100) = 5.
☛ What is a Prime Number?

What are the Methods to Find GCF of 55 and 100?

There are three commonly used methods to find the GCF of 55 and 100.

By Prime Factorization
By Long Division
By Euclidean Algorithm

What is the Relation Between LCM and GCF of 55, 100?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 55 and 100, i.e. GCF × LCM = 55 × 100.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum