What is the Greatest Common Factor of 29946 and 29964?

Greatest common factor (GCF) of 29946 and 29964 is 6.

GCF(29946,29964) = 6

We will now calculate the prime factors of 29946 and 29964, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29946 and 29964.

How to find the GCF of 29946 and 29964?

We will first find the prime factorization of 29946 and 29964. After we will calculate the factors of 29946 and 29964 and find the biggest common factor number .

Step-1: Prime Factorization of 29946

Prime factors of 29946 are 2, 3, 7, 23, 31. Prime factorization of 29946 in exponential form is:

29946 = 2¹ × 3¹ × 7¹ × 23¹ × 31¹

Step-2: 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-3: Factors of 29946

List of positive integer factors of 29946 that divides 29946 without a remainder.

1, 2, 3, 6, 7, 14, 21, 23, 31, 42, 46, 62, 69, 93, 138, 161, 186, 217, 322, 434, 483, 651, 713, 966, 1302, 1426, 2139, 4278, 4991, 9982, 14973

Step-4: Factors of 29964

List of positive integer factors of 29964 that divides 29946 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29946 and 29964. The biggest common factor number is the GCF number.
So the greatest common factor 29946 and 29964 is 6.

Also check out the Least Common Multiple of 29946 and 29964