What is the Greatest Common Factor of 782 and 802?

Greatest common factor (GCF) of 782 and 802 is 2.

GCF(782,802) = 2

We will now calculate the prime factors of 782 and 802, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 782 and 802.

How to find the GCF of 782 and 802?

We will first find the prime factorization of 782 and 802. After we will calculate the factors of 782 and 802 and find the biggest common factor number .

Step-1: Prime Factorization of 782

Prime factors of 782 are 2, 17, 23. Prime factorization of 782 in exponential form is:

782 = 2¹ × 17¹ × 23¹

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 782

List of positive integer factors of 782 that divides 782 without a remainder.

1, 2, 17, 23, 34, 46, 391

Step-4: Factors of 802

List of positive integer factors of 802 that divides 782 without a remainder.

1, 2, 401

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 782 and 802. The biggest common factor number is the GCF number.
So the greatest common factor 782 and 802 is 2.

Also check out the Least Common Multiple of 782 and 802