What is the Greatest Common Factor of 784 and 802?

Greatest common factor (GCF) of 784 and 802 is 2.

GCF(784,802) = 2

We will now calculate the prime factors of 784 and 802, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 784 and 802.

How to find the GCF of 784 and 802?

We will first find the prime factorization of 784 and 802. After we will calculate the factors of 784 and 802 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 802

Prime factors of 802 are 2, 401. Prime factorization of 802 in exponential form is:

802 = 2¹ × 401¹

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 802

List of positive integer factors of 802 that divides 784 without a remainder.

1, 2, 401

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 784 and 802. The biggest common factor number is the GCF number.
So the greatest common factor 784 and 802 is 2.

Also check out the Least Common Multiple of 784 and 802