What is the Greatest Common Factor of 39096 and 39100?

Greatest common factor (GCF) of 39096 and 39100 is 4.

GCF(39096,39100) = 4

We will now calculate the prime factors of 39096 and 39100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39096 and 39100.

How to find the GCF of 39096 and 39100?

We will first find the prime factorization of 39096 and 39100. After we will calculate the factors of 39096 and 39100 and find the biggest common factor number .

Step-1: Prime Factorization of 39096

Prime factors of 39096 are 2, 3, 181. Prime factorization of 39096 in exponential form is:

39096 = 2³ × 3³ × 181¹

Step-2: Prime Factorization of 39100

Prime factors of 39100 are 2, 5, 17, 23. Prime factorization of 39100 in exponential form is:

39100 = 2² × 5² × 17¹ × 23¹

Step-3: Factors of 39096

List of positive integer factors of 39096 that divides 39096 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 181, 216, 362, 543, 724, 1086, 1448, 1629, 2172, 3258, 4344, 4887, 6516, 9774, 13032, 19548

Step-4: Factors of 39100

List of positive integer factors of 39100 that divides 39096 without a remainder.

1, 2, 4, 5, 10, 17, 20, 23, 25, 34, 46, 50, 68, 85, 92, 100, 115, 170, 230, 340, 391, 425, 460, 575, 782, 850, 1150, 1564, 1700, 1955, 2300, 3910, 7820, 9775, 19550

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39096 and 39100. The biggest common factor number is the GCF number.
So the greatest common factor 39096 and 39100 is 4.

Also check out the Least Common Multiple of 39096 and 39100