What is the Greatest Common Factor of 29988 and 30000?

Greatest common factor (GCF) of 29988 and 30000 is 12.

GCF(29988,30000) = 12

We will now calculate the prime factors of 29988 and 30000, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29988 and 30000.

How to find the GCF of 29988 and 30000?

We will first find the prime factorization of 29988 and 30000. After we will calculate the factors of 29988 and 30000 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 30000

Prime factors of 30000 are 2, 3, 5. Prime factorization of 30000 in exponential form is:

30000 = 2⁴ × 3¹ × 5⁴

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 30000

List of positive integer factors of 30000 that divides 29988 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 625, 750, 1000, 1200, 1250, 1500, 1875, 2000, 2500, 3000, 3750, 5000, 6000, 7500, 10000, 15000

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29988 and 30000. The biggest common factor number is the GCF number.
So the greatest common factor 29988 and 30000 is 12.

Also check out the Least Common Multiple of 29988 and 30000