What is the Greatest Common Factor of 29946 and 29961?

Greatest common factor (GCF) of 29946 and 29961 is 3.

GCF(29946,29961) = 3

We will now calculate the prime factors of 29946 and 29961, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29946 and 29961.

How to find the GCF of 29946 and 29961?

We will first find the prime factorization of 29946 and 29961. After we will calculate the factors of 29946 and 29961 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 29961

Prime factors of 29961 are 3, 3329. Prime factorization of 29961 in exponential form is:

29961 = 3² × 3329¹

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 29961

List of positive integer factors of 29961 that divides 29946 without a remainder.

1, 3, 9, 3329, 9987

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29946 and 29961. The biggest common factor number is the GCF number.
So the greatest common factor 29946 and 29961 is 3.

Also check out the Least Common Multiple of 29946 and 29961