What is the Greatest Common Factor of 14875 and 14880?

Greatest common factor (GCF) of 14875 and 14880 is 5.

GCF(14875,14880) = 5

We will now calculate the prime factors of 14875 and 14880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14875 and 14880.

How to find the GCF of 14875 and 14880?

We will first find the prime factorization of 14875 and 14880. After we will calculate the factors of 14875 and 14880 and find the biggest common factor number .

Step-1: Prime Factorization of 14875

Prime factors of 14875 are 5, 7, 17. Prime factorization of 14875 in exponential form is:

14875 = 5³ × 7¹ × 17¹

Step-2: Prime Factorization of 14880

Prime factors of 14880 are 2, 3, 5, 31. Prime factorization of 14880 in exponential form is:

14880 = 2⁵ × 3¹ × 5¹ × 31¹

Step-3: Factors of 14875

List of positive integer factors of 14875 that divides 14875 without a remainder.

1, 5, 7, 17, 25, 35, 85, 119, 125, 175, 425, 595, 875, 2125, 2975

Step-4: Factors of 14880

List of positive integer factors of 14880 that divides 14875 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 31, 32, 40, 48, 60, 62, 80, 93, 96, 120, 124, 155, 160, 186, 240, 248, 310, 372, 465, 480, 496, 620, 744, 930, 992, 1240, 1488, 1860, 2480, 2976, 3720, 4960, 7440

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14875 and 14880. The biggest common factor number is the GCF number.
So the greatest common factor 14875 and 14880 is 5.

Also check out the Least Common Multiple of 14875 and 14880