What is the Greatest Common Factor of 83504 and 83514?

Greatest common factor (GCF) of 83504 and 83514 is 2.

GCF(83504,83514) = 2

We will now calculate the prime factors of 83504 and 83514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83504 and 83514.

How to find the GCF of 83504 and 83514?

We will first find the prime factorization of 83504 and 83514. After we will calculate the factors of 83504 and 83514 and find the biggest common factor number .

Step-1: Prime Factorization of 83504

Prime factors of 83504 are 2, 17, 307. Prime factorization of 83504 in exponential form is:

83504 = 2⁴ × 17¹ × 307¹

Step-2: Prime Factorization of 83514

Prime factors of 83514 are 2, 3, 31, 449. Prime factorization of 83514 in exponential form is:

83514 = 2¹ × 3¹ × 31¹ × 449¹

Step-3: Factors of 83504

List of positive integer factors of 83504 that divides 83504 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 136, 272, 307, 614, 1228, 2456, 4912, 5219, 10438, 20876, 41752

Step-4: Factors of 83514

List of positive integer factors of 83514 that divides 83504 without a remainder.

1, 2, 3, 6, 31, 62, 93, 186, 449, 898, 1347, 2694, 13919, 27838, 41757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83504 and 83514. The biggest common factor number is the GCF number.
So the greatest common factor 83504 and 83514 is 2.

Also check out the Least Common Multiple of 83504 and 83514