What is the Greatest Common Factor of 39585 and 39598?

Greatest common factor (GCF) of 39585 and 39598 is 13.

GCF(39585,39598) = 13

We will now calculate the prime factors of 39585 and 39598, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39585 and 39598.

How to find the GCF of 39585 and 39598?

We will first find the prime factorization of 39585 and 39598. After we will calculate the factors of 39585 and 39598 and find the biggest common factor number .

Step-1: Prime Factorization of 39585

Prime factors of 39585 are 3, 5, 7, 13, 29. Prime factorization of 39585 in exponential form is:

39585 = 3¹ × 5¹ × 7¹ × 13¹ × 29¹

Step-2: Prime Factorization of 39598

Prime factors of 39598 are 2, 13, 1523. Prime factorization of 39598 in exponential form is:

39598 = 2¹ × 13¹ × 1523¹

Step-3: Factors of 39585

List of positive integer factors of 39585 that divides 39585 without a remainder.

1, 3, 5, 7, 13, 15, 21, 29, 35, 39, 65, 87, 91, 105, 145, 195, 203, 273, 377, 435, 455, 609, 1015, 1131, 1365, 1885, 2639, 3045, 5655, 7917, 13195

Step-4: Factors of 39598

List of positive integer factors of 39598 that divides 39585 without a remainder.

1, 2, 13, 26, 1523, 3046, 19799

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39585 and 39598. The biggest common factor number is the GCF number.
So the greatest common factor 39585 and 39598 is 13.

Also check out the Least Common Multiple of 39585 and 39598