What is the Greatest Common Factor of 58290 and 58310?

Greatest common factor (GCF) of 58290 and 58310 is 10.

GCF(58290,58310) = 10

We will now calculate the prime factors of 58290 and 58310, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58290 and 58310.

How to find the GCF of 58290 and 58310?

We will first find the prime factorization of 58290 and 58310. After we will calculate the factors of 58290 and 58310 and find the biggest common factor number .

Step-1: Prime Factorization of 58290

Prime factors of 58290 are 2, 3, 5, 29, 67. Prime factorization of 58290 in exponential form is:

58290 = 2¹ × 3¹ × 5¹ × 29¹ × 67¹

Step-2: Prime Factorization of 58310

Prime factors of 58310 are 2, 5, 7, 17. Prime factorization of 58310 in exponential form is:

58310 = 2¹ × 5¹ × 7³ × 17¹

Step-3: Factors of 58290

List of positive integer factors of 58290 that divides 58290 without a remainder.

1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 67, 87, 134, 145, 174, 201, 290, 335, 402, 435, 670, 870, 1005, 1943, 2010, 3886, 5829, 9715, 11658, 19430, 29145

Step-4: Factors of 58310

List of positive integer factors of 58310 that divides 58290 without a remainder.

1, 2, 5, 7, 10, 14, 17, 34, 35, 49, 70, 85, 98, 119, 170, 238, 245, 343, 490, 595, 686, 833, 1190, 1666, 1715, 3430, 4165, 5831, 8330, 11662, 29155

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58290 and 58310. The biggest common factor number is the GCF number.
So the greatest common factor 58290 and 58310 is 10.

Also check out the Least Common Multiple of 58290 and 58310