What is the Greatest Common Factor of 29971 and 29988?

Greatest common factor (GCF) of 29971 and 29988 is 17.

GCF(29971,29988) = 17

We will now calculate the prime factors of 29971 and 29988, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29971 and 29988.

How to find the GCF of 29971 and 29988?

We will first find the prime factorization of 29971 and 29988. After we will calculate the factors of 29971 and 29988 and find the biggest common factor number .

Step-1: Prime Factorization of 29971

Prime factors of 29971 are 17, 41, 43. Prime factorization of 29971 in exponential form is:

29971 = 17¹ × 41¹ × 43¹

Step-2: 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-3: Factors of 29971

List of positive integer factors of 29971 that divides 29971 without a remainder.

1, 17, 41, 43, 697, 731, 1763

Step-4: Factors of 29988

List of positive integer factors of 29988 that divides 29971 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29971 and 29988. The biggest common factor number is the GCF number.
So the greatest common factor 29971 and 29988 is 17.

Also check out the Least Common Multiple of 29971 and 29988