What is the Greatest Common Factor of 29964 and 29970?

Greatest common factor (GCF) of 29964 and 29970 is 6.

GCF(29964,29970) = 6

We will now calculate the prime factors of 29964 and 29970, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29964 and 29970.

How to find the GCF of 29964 and 29970?

We will first find the prime factorization of 29964 and 29970. After we will calculate the factors of 29964 and 29970 and find the biggest common factor number .

Step-1: Prime Factorization of 29964

Prime factors of 29964 are 2, 3, 11, 227. Prime factorization of 29964 in exponential form is:

29964 = 2² × 3¹ × 11¹ × 227¹

Step-2: 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-3: Factors of 29964

List of positive integer factors of 29964 that divides 29964 without a remainder.

1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132, 227, 454, 681, 908, 1362, 2497, 2724, 4994, 7491, 9988, 14982

Step-4: Factors of 29970

List of positive integer factors of 29970 that divides 29964 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29964 and 29970. The biggest common factor number is the GCF number.
So the greatest common factor 29964 and 29970 is 6.

Also check out the Least Common Multiple of 29964 and 29970