What is the Greatest Common Factor of 784 and 800?

Greatest common factor (GCF) of 784 and 800 is 16.

GCF(784,800) = 16

We will now calculate the prime factors of 784 and 800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 784 and 800.

How to find the GCF of 784 and 800?

We will first find the prime factorization of 784 and 800. After we will calculate the factors of 784 and 800 and find the biggest common factor number .

Step-1: Prime Factorization of 784

Prime factors of 784 are 2, 7. Prime factorization of 784 in exponential form is:

784 = 2⁴ × 7²

Step-2: Prime Factorization of 800

Prime factors of 800 are 2, 5. Prime factorization of 800 in exponential form is:

800 = 2⁵ × 5²

Step-3: Factors of 784

List of positive integer factors of 784 that divides 784 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392

Step-4: Factors of 800

List of positive integer factors of 800 that divides 784 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 784 and 800. The biggest common factor number is the GCF number.
So the greatest common factor 784 and 800 is 16.

Also check out the Least Common Multiple of 784 and 800