What is the Greatest Common Factor of 35385 and 35400?

Greatest common factor (GCF) of 35385 and 35400 is 15.

GCF(35385,35400) = 15

We will now calculate the prime factors of 35385 and 35400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35385 and 35400.

How to find the GCF of 35385 and 35400?

We will first find the prime factorization of 35385 and 35400. After we will calculate the factors of 35385 and 35400 and find the biggest common factor number .

Step-1: Prime Factorization of 35385

Prime factors of 35385 are 3, 5, 7, 337. Prime factorization of 35385 in exponential form is:

35385 = 3¹ × 5¹ × 7¹ × 337¹

Step-2: Prime Factorization of 35400

Prime factors of 35400 are 2, 3, 5, 59. Prime factorization of 35400 in exponential form is:

35400 = 2³ × 3¹ × 5² × 59¹

Step-3: Factors of 35385

List of positive integer factors of 35385 that divides 35385 without a remainder.

1, 3, 5, 7, 15, 21, 35, 105, 337, 1011, 1685, 2359, 5055, 7077, 11795

Step-4: Factors of 35400

List of positive integer factors of 35400 that divides 35385 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 59, 60, 75, 100, 118, 120, 150, 177, 200, 236, 295, 300, 354, 472, 590, 600, 708, 885, 1180, 1416, 1475, 1770, 2360, 2950, 3540, 4425, 5900, 7080, 8850, 11800, 17700

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35385 and 35400. The biggest common factor number is the GCF number.
So the greatest common factor 35385 and 35400 is 15.

Also check out the Least Common Multiple of 35385 and 35400