What is the Greatest Common Factor of 29940 and 29946?

Greatest common factor (GCF) of 29940 and 29946 is 6.

GCF(29940,29946) = 6

We will now calculate the prime factors of 29940 and 29946, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29940 and 29946.

How to find the GCF of 29940 and 29946?

We will first find the prime factorization of 29940 and 29946. After we will calculate the factors of 29940 and 29946 and find the biggest common factor number .

Step-1: Prime Factorization of 29940

Prime factors of 29940 are 2, 3, 5, 499. Prime factorization of 29940 in exponential form is:

29940 = 2² × 3¹ × 5¹ × 499¹

Step-2: 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-3: Factors of 29940

List of positive integer factors of 29940 that divides 29940 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 499, 998, 1497, 1996, 2495, 2994, 4990, 5988, 7485, 9980, 14970

Step-4: Factors of 29946

List of positive integer factors of 29946 that divides 29940 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29940 and 29946. The biggest common factor number is the GCF number.
So the greatest common factor 29940 and 29946 is 6.

Also check out the Least Common Multiple of 29940 and 29946