What is the Greatest Common Factor of 58289 and 58300?

Greatest common factor (GCF) of 58289 and 58300 is 11.

GCF(58289,58300) = 11

We will now calculate the prime factors of 58289 and 58300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58289 and 58300.

How to find the GCF of 58289 and 58300?

We will first find the prime factorization of 58289 and 58300. After we will calculate the factors of 58289 and 58300 and find the biggest common factor number .

Step-1: Prime Factorization of 58289

Prime factors of 58289 are 7, 11, 757. Prime factorization of 58289 in exponential form is:

58289 = 7¹ × 11¹ × 757¹

Step-2: Prime Factorization of 58300

Prime factors of 58300 are 2, 5, 11, 53. Prime factorization of 58300 in exponential form is:

58300 = 2² × 5² × 11¹ × 53¹

Step-3: Factors of 58289

List of positive integer factors of 58289 that divides 58289 without a remainder.

1, 7, 11, 77, 757, 5299, 8327

Step-4: Factors of 58300

List of positive integer factors of 58300 that divides 58289 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 25, 44, 50, 53, 55, 100, 106, 110, 212, 220, 265, 275, 530, 550, 583, 1060, 1100, 1166, 1325, 2332, 2650, 2915, 5300, 5830, 11660, 14575, 29150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58289 and 58300. The biggest common factor number is the GCF number.
So the greatest common factor 58289 and 58300 is 11.

Also check out the Least Common Multiple of 58289 and 58300