What is the Greatest Common Factor of 29965 and 29970?

Greatest common factor (GCF) of 29965 and 29970 is 5.

GCF(29965,29970) = 5

We will now calculate the prime factors of 29965 and 29970, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29965 and 29970.

How to find the GCF of 29965 and 29970?

We will first find the prime factorization of 29965 and 29970. After we will calculate the factors of 29965 and 29970 and find the biggest common factor number .

Step-1: Prime Factorization of 29965

Prime factors of 29965 are 5, 13, 461. Prime factorization of 29965 in exponential form is:

29965 = 5¹ × 13¹ × 461¹

Step-2: Prime Factorization of 29970

Prime factors of 29970 are 2, 3, 5, 37. Prime factorization of 29970 in exponential form is:

29970 = 2¹ × 3⁴ × 5¹ × 37¹

Step-3: Factors of 29965

List of positive integer factors of 29965 that divides 29965 without a remainder.

1, 5, 13, 65, 461, 2305, 5993

Step-4: Factors of 29970

List of positive integer factors of 29970 that divides 29965 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 37, 45, 54, 74, 81, 90, 111, 135, 162, 185, 222, 270, 333, 370, 405, 555, 666, 810, 999, 1110, 1665, 1998, 2997, 3330, 4995, 5994, 9990, 14985

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29965 and 29970. The biggest common factor number is the GCF number.
So the greatest common factor 29965 and 29970 is 5.

Also check out the Least Common Multiple of 29965 and 29970