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

GCF of 64 and 100

GCF of 64 and 100 is the largest possible number that divides 64 and 100 exactly without any remainder. The factors of 64 and 100 are 1, 2, 4, 8, 16, 32, 64 and 1, 2, 4, 5, 10, 20, 25, 50, 100 respectively. There are 3 commonly used methods to find the GCF of 64 and 100 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 64 and 100
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 64 and 100?

Answer: GCF of 64 and 100 is 4.

Explanation:

The GCF of two non-zero integers, x(64) and y(100), is the greatest positive integer m(4) that divides both x(64) and y(100) without any remainder.

Methods to Find GCF of 64 and 100

Let's look at the different methods for finding the GCF of 64 and 100.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

GCF of 64 and 100 by Listing Common Factors

Factors of 64: 1, 2, 4, 8, 16, 32, 64
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

There are 3 common factors of 64 and 100, that are 1, 2, and 4. Therefore, the greatest common factor of 64 and 100 is 4.

GCF of 64 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 = 64

GCF(100, 64) = GCF(64, 100 mod 64) = GCF(64, 36)
GCF(64, 36) = GCF(36, 64 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 64 and 100 is 4.

GCF of 64 and 100 by Long Division

GCF of 64 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 64 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (64) by the remainder (36).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 64 and 100.

☛ Also Check:

GCF of 64 and 100 Examples

Example 1: The product of two numbers is 6400. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 6400
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 6400/4
Therefore, the LCM is 1600.
Example 2: For two numbers, GCF = 4 and LCM = 1600. If one number is 64, find the other number.

Solution:

Given: GCF (x, 64) = 4 and LCM (x, 64) = 1600
∵ GCF × LCM = 64 × (x)
⇒ x = (GCF × LCM)/64
⇒ x = (4 × 1600)/64
⇒ x = 100
Therefore, the other number is 100.
Example 3: Find the greatest number that divides 64 and 100 exactly.

Solution:

The greatest number that divides 64 and 100 exactly is their greatest common factor, i.e. GCF of 64 and 100.
⇒ Factors of 64 and 100:
- Factors of 64 = 1, 2, 4, 8, 16, 32, 64
- Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
Therefore, the GCF of 64 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 64 and 100

What is the GCF of 64 and 100?

The GCF of 64 and 100 is 4. To calculate the greatest common factor (GCF) of 64 and 100, we need to factor each number (factors of 64 = 1, 2, 4, 8, 16, 32, 64; factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100) and choose the greatest factor that exactly divides both 64 and 100, i.e., 4.

What is the Relation Between LCM and GCF of 64, 100?

The following equation can be used to express the relation between LCM and GCF of 64 and 100, i.e. GCF × LCM = 64 × 100.

If the GCF of 100 and 64 is 4, Find its LCM.

GCF(100, 64) × LCM(100, 64) = 100 × 64
Since the GCF of 100 and 64 = 4
⇒ 4 × LCM(100, 64) = 6400
Therefore, LCM = 1600
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 64 and 100?

There are three commonly used methods to find the GCF of 64 and 100.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the GCF of 64 and 100 by Long Division Method?

To find the GCF of 64, 100 using long division method, 100 is divided by 64. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

How to Find the GCF of 64 and 100 by Prime Factorization?

To find the GCF of 64 and 100, we will find the prime factorization of the given numbers, i.e. 64 = 2 × 2 × 2 × 2 × 2 × 2; 100 = 2 × 2 × 5 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 64 and 100. Hence, GCF(64, 100) = 2 × 2 = 4
☛ What is a Prime Number?

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum