What is the Greatest Common Factor of 29988 and 29997?

Greatest common factor (GCF) of 29988 and 29997 is 9.

GCF(29988,29997) = 9

We will now calculate the prime factors of 29988 and 29997, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29988 and 29997.

How to find the GCF of 29988 and 29997?

We will first find the prime factorization of 29988 and 29997. After we will calculate the factors of 29988 and 29997 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 29997

Prime factors of 29997 are 3, 11, 101. Prime factorization of 29997 in exponential form is:

29997 = 3³ × 11¹ × 101¹

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 29997

List of positive integer factors of 29997 that divides 29988 without a remainder.

1, 3, 9, 11, 27, 33, 99, 101, 297, 303, 909, 1111, 2727, 3333, 9999

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29988 and 29997. The biggest common factor number is the GCF number.
So the greatest common factor 29988 and 29997 is 9.

Also check out the Least Common Multiple of 29988 and 29997