What is the Greatest Common Factor of 39100 and 39104?

Greatest common factor (GCF) of 39100 and 39104 is 4.

GCF(39100,39104) = 4

We will now calculate the prime factors of 39100 and 39104, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39100 and 39104.

How to find the GCF of 39100 and 39104?

We will first find the prime factorization of 39100 and 39104. After we will calculate the factors of 39100 and 39104 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 39104

Prime factors of 39104 are 2, 13, 47. Prime factorization of 39104 in exponential form is:

39104 = 2⁶ × 13¹ × 47¹

Step-3: Factors of 39100

List of positive integer factors of 39100 that divides 39100 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

Step-4: Factors of 39104

List of positive integer factors of 39104 that divides 39100 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 47, 52, 64, 94, 104, 188, 208, 376, 416, 611, 752, 832, 1222, 1504, 2444, 3008, 4888, 9776, 19552

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39100 and 39104. The biggest common factor number is the GCF number.
So the greatest common factor 39100 and 39104 is 4.

Also check out the Least Common Multiple of 39100 and 39104