What is the Greatest Common Factor of 52500 and 52514?

Greatest common factor (GCF) of 52500 and 52514 is 14.

GCF(52500,52514) = 14

We will now calculate the prime factors of 52500 and 52514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 52500 and 52514.

How to find the GCF of 52500 and 52514?

We will first find the prime factorization of 52500 and 52514. After we will calculate the factors of 52500 and 52514 and find the biggest common factor number .

Step-1: Prime Factorization of 52500

Prime factors of 52500 are 2, 3, 5, 7. Prime factorization of 52500 in exponential form is:

52500 = 2² × 3¹ × 5⁴ × 7¹

Step-2: Prime Factorization of 52514

Prime factors of 52514 are 2, 7, 11, 31. Prime factorization of 52514 in exponential form is:

52514 = 2¹ × 7¹ × 11² × 31¹

Step-3: Factors of 52500

List of positive integer factors of 52500 that divides 52500 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 125, 140, 150, 175, 210, 250, 300, 350, 375, 420, 500, 525, 625, 700, 750, 875, 1050, 1250, 1500, 1750, 1875, 2100, 2500, 2625, 3500, 3750, 4375, 5250, 7500, 8750, 10500, 13125, 17500, 26250

Step-4: Factors of 52514

List of positive integer factors of 52514 that divides 52500 without a remainder.

1, 2, 7, 11, 14, 22, 31, 62, 77, 121, 154, 217, 242, 341, 434, 682, 847, 1694, 2387, 3751, 4774, 7502, 26257

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 52500 and 52514. The biggest common factor number is the GCF number.
So the greatest common factor 52500 and 52514 is 14.

Also check out the Least Common Multiple of 52500 and 52514