What is the Greatest Common Factor of 29970 and 29986?

Greatest common factor (GCF) of 29970 and 29986 is 2.

GCF(29970,29986) = 2

We will now calculate the prime factors of 29970 and 29986, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29970 and 29986.

How to find the GCF of 29970 and 29986?

We will first find the prime factorization of 29970 and 29986. After we will calculate the factors of 29970 and 29986 and find the biggest common factor number .

Step-1: Prime Factorization of 29970

Prime factors of 29970 are 2, 3, 5, 37. Prime factorization of 29970 in exponential form is:

29970 = 2¹ × 3⁴ × 5¹ × 37¹

Step-2: Prime Factorization of 29986

Prime factors of 29986 are 2, 11, 29, 47. Prime factorization of 29986 in exponential form is:

29986 = 2¹ × 11¹ × 29¹ × 47¹

Step-3: Factors of 29970

List of positive integer factors of 29970 that divides 29970 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 37, 45, 54, 74, 81, 90, 111, 135, 162, 185, 222, 270, 333, 370, 405, 555, 666, 810, 999, 1110, 1665, 1998, 2997, 3330, 4995, 5994, 9990, 14985

Step-4: Factors of 29986

List of positive integer factors of 29986 that divides 29970 without a remainder.

1, 2, 11, 22, 29, 47, 58, 94, 319, 517, 638, 1034, 1363, 2726, 14993

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29970 and 29986. The biggest common factor number is the GCF number.
So the greatest common factor 29970 and 29986 is 2.

Also check out the Least Common Multiple of 29970 and 29986