What is the Greatest Common Factor of 29946 and 29962?

Greatest common factor (GCF) of 29946 and 29962 is 2.

GCF(29946,29962) = 2

We will now calculate the prime factors of 29946 and 29962, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29946 and 29962.

How to find the GCF of 29946 and 29962?

We will first find the prime factorization of 29946 and 29962. After we will calculate the factors of 29946 and 29962 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 29962

Prime factors of 29962 are 2, 71, 211. Prime factorization of 29962 in exponential form is:

29962 = 2¹ × 71¹ × 211¹

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 29962

List of positive integer factors of 29962 that divides 29946 without a remainder.

1, 2, 71, 142, 211, 422, 14981

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29946 and 29962. The biggest common factor number is the GCF number.
So the greatest common factor 29946 and 29962 is 2.

Also check out the Least Common Multiple of 29946 and 29962