What is the Greatest Common Factor of 29988 and 30005?

Greatest common factor (GCF) of 29988 and 30005 is 17.

GCF(29988,30005) = 17

We will now calculate the prime factors of 29988 and 30005, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29988 and 30005.

How to find the GCF of 29988 and 30005?

We will first find the prime factorization of 29988 and 30005. After we will calculate the factors of 29988 and 30005 and find the biggest common factor number .

Step-1: Prime Factorization of 29988

Prime factors of 29988 are 2, 3, 7, 17. Prime factorization of 29988 in exponential form is:

29988 = 2² × 3² × 7² × 17¹

Step-2: Prime Factorization of 30005

Prime factors of 30005 are 5, 17, 353. Prime factorization of 30005 in exponential form is:

30005 = 5¹ × 17¹ × 353¹

Step-3: Factors of 29988

List of positive integer factors of 29988 that divides 29988 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 17, 18, 21, 28, 34, 36, 42, 49, 51, 63, 68, 84, 98, 102, 119, 126, 147, 153, 196, 204, 238, 252, 294, 306, 357, 441, 476, 588, 612, 714, 833, 882, 1071, 1428, 1666, 1764, 2142, 2499, 3332, 4284, 4998, 7497, 9996, 14994

Step-4: Factors of 30005

List of positive integer factors of 30005 that divides 29988 without a remainder.

1, 5, 17, 85, 353, 1765, 6001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29988 and 30005. The biggest common factor number is the GCF number.
So the greatest common factor 29988 and 30005 is 17.

Also check out the Least Common Multiple of 29988 and 30005