What is the Greatest Common Factor of 29985 and 29991?

Greatest common factor (GCF) of 29985 and 29991 is 3.

GCF(29985,29991) = 3

We will now calculate the prime factors of 29985 and 29991, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29985 and 29991.

How to find the GCF of 29985 and 29991?

We will first find the prime factorization of 29985 and 29991. After we will calculate the factors of 29985 and 29991 and find the biggest common factor number .

Step-1: Prime Factorization of 29985

Prime factors of 29985 are 3, 5, 1999. Prime factorization of 29985 in exponential form is:

29985 = 3¹ × 5¹ × 1999¹

Step-2: Prime Factorization of 29991

Prime factors of 29991 are 3, 13, 769. Prime factorization of 29991 in exponential form is:

29991 = 3¹ × 13¹ × 769¹

Step-3: Factors of 29985

List of positive integer factors of 29985 that divides 29985 without a remainder.

1, 3, 5, 15, 1999, 5997, 9995

Step-4: Factors of 29991

List of positive integer factors of 29991 that divides 29985 without a remainder.

1, 3, 13, 39, 769, 2307, 9997

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29985 and 29991. The biggest common factor number is the GCF number.
So the greatest common factor 29985 and 29991 is 3.

Also check out the Least Common Multiple of 29985 and 29991