What is the Greatest Common Factor of 14750 and 14760?

Greatest common factor (GCF) of 14750 and 14760 is 10.

GCF(14750,14760) = 10

We will now calculate the prime factors of 14750 and 14760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14750 and 14760.

How to find the GCF of 14750 and 14760?

We will first find the prime factorization of 14750 and 14760. After we will calculate the factors of 14750 and 14760 and find the biggest common factor number .

Step-1: Prime Factorization of 14750

Prime factors of 14750 are 2, 5, 59. Prime factorization of 14750 in exponential form is:

14750 = 2¹ × 5³ × 59¹

Step-2: Prime Factorization of 14760

Prime factors of 14760 are 2, 3, 5, 41. Prime factorization of 14760 in exponential form is:

14760 = 2³ × 3² × 5¹ × 41¹

Step-3: Factors of 14750

List of positive integer factors of 14750 that divides 14750 without a remainder.

1, 2, 5, 10, 25, 50, 59, 118, 125, 250, 295, 590, 1475, 2950, 7375

Step-4: Factors of 14760

List of positive integer factors of 14760 that divides 14750 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 41, 45, 60, 72, 82, 90, 120, 123, 164, 180, 205, 246, 328, 360, 369, 410, 492, 615, 738, 820, 984, 1230, 1476, 1640, 1845, 2460, 2952, 3690, 4920, 7380

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14750 and 14760. The biggest common factor number is the GCF number.
So the greatest common factor 14750 and 14760 is 10.

Also check out the Least Common Multiple of 14750 and 14760