What is the Greatest Common Factor of 52500 and 52509?

Greatest common factor (GCF) of 52500 and 52509 is 3.

GCF(52500,52509) = 3

We will now calculate the prime factors of 52500 and 52509, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 52500 and 52509.

How to find the GCF of 52500 and 52509?

We will first find the prime factorization of 52500 and 52509. After we will calculate the factors of 52500 and 52509 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 52509

Prime factors of 52509 are 3, 23, 761. Prime factorization of 52509 in exponential form is:

52509 = 3¹ × 23¹ × 761¹

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 52509

List of positive integer factors of 52509 that divides 52500 without a remainder.

1, 3, 23, 69, 761, 2283, 17503

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 52500 and 52509. The biggest common factor number is the GCF number.
So the greatest common factor 52500 and 52509 is 3.

Also check out the Least Common Multiple of 52500 and 52509