What is the Greatest Common Factor of 59970 and 59985?

Greatest common factor (GCF) of 59970 and 59985 is 15.

GCF(59970,59985) = 15

We will now calculate the prime factors of 59970 and 59985, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 59970 and 59985.

How to find the GCF of 59970 and 59985?

We will first find the prime factorization of 59970 and 59985. After we will calculate the factors of 59970 and 59985 and find the biggest common factor number .

Step-1: Prime Factorization of 59970

Prime factors of 59970 are 2, 3, 5, 1999. Prime factorization of 59970 in exponential form is:

59970 = 2¹ × 3¹ × 5¹ × 1999¹

Step-2: Prime Factorization of 59985

Prime factors of 59985 are 3, 5, 31, 43. Prime factorization of 59985 in exponential form is:

59985 = 3² × 5¹ × 31¹ × 43¹

Step-3: Factors of 59970

List of positive integer factors of 59970 that divides 59970 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 1999, 3998, 5997, 9995, 11994, 19990, 29985

Step-4: Factors of 59985

List of positive integer factors of 59985 that divides 59970 without a remainder.

1, 3, 5, 9, 15, 31, 43, 45, 93, 129, 155, 215, 279, 387, 465, 645, 1333, 1395, 1935, 3999, 6665, 11997, 19995

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 59970 and 59985. The biggest common factor number is the GCF number.
So the greatest common factor 59970 and 59985 is 15.

Also check out the Least Common Multiple of 59970 and 59985