What is the Greatest Common Factor of 802 and 814?

Greatest common factor (GCF) of 802 and 814 is 2.

GCF(802,814) = 2

We will now calculate the prime factors of 802 and 814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 802 and 814.

How to find the GCF of 802 and 814?

We will first find the prime factorization of 802 and 814. After we will calculate the factors of 802 and 814 and find the biggest common factor number .

Step-1: Prime Factorization of 802

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

802 = 2¹ × 401¹

Step-2: Prime Factorization of 814

Prime factors of 814 are 2, 11, 37. Prime factorization of 814 in exponential form is:

814 = 2¹ × 11¹ × 37¹

Step-3: Factors of 802

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

1, 2, 401

Step-4: Factors of 814

List of positive integer factors of 814 that divides 802 without a remainder.

1, 2, 11, 22, 37, 74, 407

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 802 and 814. The biggest common factor number is the GCF number.
So the greatest common factor 802 and 814 is 2.

Also check out the Least Common Multiple of 802 and 814