What is the Greatest Common Factor of 71385 and 71400?

Greatest common factor (GCF) of 71385 and 71400 is 15.

GCF(71385,71400) = 15

We will now calculate the prime factors of 71385 and 71400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71385 and 71400.

How to find the GCF of 71385 and 71400?

We will first find the prime factorization of 71385 and 71400. After we will calculate the factors of 71385 and 71400 and find the biggest common factor number .

Step-1: Prime Factorization of 71385

Prime factors of 71385 are 3, 5, 4759. Prime factorization of 71385 in exponential form is:

71385 = 3¹ × 5¹ × 4759¹

Step-2: Prime Factorization of 71400

Prime factors of 71400 are 2, 3, 5, 7, 17. Prime factorization of 71400 in exponential form is:

71400 = 2³ × 3¹ × 5² × 7¹ × 17¹

Step-3: Factors of 71385

List of positive integer factors of 71385 that divides 71385 without a remainder.

1, 3, 5, 15, 4759, 14277, 23795

Step-4: Factors of 71400

List of positive integer factors of 71400 that divides 71385 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 17, 20, 21, 24, 25, 28, 30, 34, 35, 40, 42, 50, 51, 56, 60, 68, 70, 75, 84, 85, 100, 102, 105, 119, 120, 136, 140, 150, 168, 170, 175, 200, 204, 210, 238, 255, 280, 300, 340, 350, 357, 408, 420, 425, 476, 510, 525, 595, 600, 680, 700, 714, 840, 850, 952, 1020, 1050, 1190, 1275, 1400, 1428, 1700, 1785, 2040, 2100, 2380, 2550, 2856, 2975, 3400, 3570, 4200, 4760, 5100, 5950, 7140, 8925, 10200, 11900, 14280, 17850, 23800, 35700

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71385 and 71400. The biggest common factor number is the GCF number.
So the greatest common factor 71385 and 71400 is 15.

Also check out the Least Common Multiple of 71385 and 71400