What is the Greatest Common Factor of 784 and 798?

Greatest common factor (GCF) of 784 and 798 is 14.

GCF(784,798) = 14

We will now calculate the prime factors of 784 and 798, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 784 and 798.

How to find the GCF of 784 and 798?

We will first find the prime factorization of 784 and 798. After we will calculate the factors of 784 and 798 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 798

Prime factors of 798 are 2, 3, 7, 19. Prime factorization of 798 in exponential form is:

798 = 2¹ × 3¹ × 7¹ × 19¹

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 798

List of positive integer factors of 798 that divides 784 without a remainder.

1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 57, 114, 133, 266, 399

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 784 and 798. The biggest common factor number is the GCF number.
So the greatest common factor 784 and 798 is 14.

Also check out the Least Common Multiple of 784 and 798