What is the Greatest Common Factor of 58205 and 58212?

Greatest common factor (GCF) of 58205 and 58212 is 7.

GCF(58205,58212) = 7

We will now calculate the prime factors of 58205 and 58212, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 58205 and 58212.

How to find the GCF of 58205 and 58212?

We will first find the prime factorization of 58205 and 58212. After we will calculate the factors of 58205 and 58212 and find the biggest common factor number .

Step-1: Prime Factorization of 58205

Prime factors of 58205 are 5, 7, 1663. Prime factorization of 58205 in exponential form is:

58205 = 5¹ × 7¹ × 1663¹

Step-2: Prime Factorization of 58212

Prime factors of 58212 are 2, 3, 7, 11. Prime factorization of 58212 in exponential form is:

58212 = 2² × 3³ × 7² × 11¹

Step-3: Factors of 58205

List of positive integer factors of 58205 that divides 58205 without a remainder.

1, 5, 7, 35, 1663, 8315, 11641

Step-4: Factors of 58212

List of positive integer factors of 58212 that divides 58205 without a remainder.

1, 2, 3, 4, 6, 7, 9, 11, 12, 14, 18, 21, 22, 27, 28, 33, 36, 42, 44, 49, 54, 63, 66, 77, 84, 98, 99, 108, 126, 132, 147, 154, 189, 196, 198, 231, 252, 294, 297, 308, 378, 396, 441, 462, 539, 588, 594, 693, 756, 882, 924, 1078, 1188, 1323, 1386, 1617, 1764, 2079, 2156, 2646, 2772, 3234, 4158, 4851, 5292, 6468, 8316, 9702, 14553, 19404, 29106

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 58205 and 58212. The biggest common factor number is the GCF number.
So the greatest common factor 58205 and 58212 is 7.

Also check out the Least Common Multiple of 58205 and 58212