What is the Greatest Common Factor of 14280 and 14297?

Greatest common factor (GCF) of 14280 and 14297 is 17.

GCF(14280,14297) = 17

We will now calculate the prime factors of 14280 and 14297, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14280 and 14297.

How to find the GCF of 14280 and 14297?

We will first find the prime factorization of 14280 and 14297. After we will calculate the factors of 14280 and 14297 and find the biggest common factor number .

Step-1: Prime Factorization of 14280

Prime factors of 14280 are 2, 3, 5, 7, 17. Prime factorization of 14280 in exponential form is:

14280 = 2³ × 3¹ × 5¹ × 7¹ × 17¹

Step-2: Prime Factorization of 14297

Prime factors of 14297 are 17, 29. Prime factorization of 14297 in exponential form is:

14297 = 17¹ × 29²

Step-3: Factors of 14280

List of positive integer factors of 14280 that divides 14280 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 17, 20, 21, 24, 28, 30, 34, 35, 40, 42, 51, 56, 60, 68, 70, 84, 85, 102, 105, 119, 120, 136, 140, 168, 170, 204, 210, 238, 255, 280, 340, 357, 408, 420, 476, 510, 595, 680, 714, 840, 952, 1020, 1190, 1428, 1785, 2040, 2380, 2856, 3570, 4760, 7140

Step-4: Factors of 14297

List of positive integer factors of 14297 that divides 14280 without a remainder.

1, 17, 29, 493, 841

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14280 and 14297. The biggest common factor number is the GCF number.
So the greatest common factor 14280 and 14297 is 17.

Also check out the Least Common Multiple of 14280 and 14297