What is the Greatest Common Factor of 29988 and 30002?

Greatest common factor (GCF) of 29988 and 30002 is 14.

GCF(29988,30002) = 14

We will now calculate the prime factors of 29988 and 30002, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29988 and 30002.

How to find the GCF of 29988 and 30002?

We will first find the prime factorization of 29988 and 30002. After we will calculate the factors of 29988 and 30002 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 30002

Prime factors of 30002 are 2, 7, 2143. Prime factorization of 30002 in exponential form is:

30002 = 2¹ × 7¹ × 2143¹

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 30002

List of positive integer factors of 30002 that divides 29988 without a remainder.

1, 2, 7, 14, 2143, 4286, 15001

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29988 and 30002. The biggest common factor number is the GCF number.
So the greatest common factor 29988 and 30002 is 14.

Also check out the Least Common Multiple of 29988 and 30002