What is the Greatest Common Factor of 35880 and 35900?

Greatest common factor (GCF) of 35880 and 35900 is 20.

GCF(35880,35900) = 20

We will now calculate the prime factors of 35880 and 35900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35880 and 35900.

How to find the GCF of 35880 and 35900?

We will first find the prime factorization of 35880 and 35900. After we will calculate the factors of 35880 and 35900 and find the biggest common factor number .

Step-1: Prime Factorization of 35880

Prime factors of 35880 are 2, 3, 5, 13, 23. Prime factorization of 35880 in exponential form is:

35880 = 2³ × 3¹ × 5¹ × 13¹ × 23¹

Step-2: Prime Factorization of 35900

Prime factors of 35900 are 2, 5, 359. Prime factorization of 35900 in exponential form is:

35900 = 2² × 5² × 359¹

Step-3: Factors of 35880

List of positive integer factors of 35880 that divides 35880 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 20, 23, 24, 26, 30, 39, 40, 46, 52, 60, 65, 69, 78, 92, 104, 115, 120, 130, 138, 156, 184, 195, 230, 260, 276, 299, 312, 345, 390, 460, 520, 552, 598, 690, 780, 897, 920, 1196, 1380, 1495, 1560, 1794, 2392, 2760, 2990, 3588, 4485, 5980, 7176, 8970, 11960, 17940

Step-4: Factors of 35900

List of positive integer factors of 35900 that divides 35880 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 359, 718, 1436, 1795, 3590, 7180, 8975, 17950

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35880 and 35900. The biggest common factor number is the GCF number.
So the greatest common factor 35880 and 35900 is 20.

Also check out the Least Common Multiple of 35880 and 35900