What is the Greatest Common Factor of 34005 and 34020?

Greatest common factor (GCF) of 34005 and 34020 is 15.

GCF(34005,34020) = 15

We will now calculate the prime factors of 34005 and 34020, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34005 and 34020.

How to find the GCF of 34005 and 34020?

We will first find the prime factorization of 34005 and 34020. After we will calculate the factors of 34005 and 34020 and find the biggest common factor number .

Step-1: Prime Factorization of 34005

Prime factors of 34005 are 3, 5, 2267. Prime factorization of 34005 in exponential form is:

34005 = 3¹ × 5¹ × 2267¹

Step-2: Prime Factorization of 34020

Prime factors of 34020 are 2, 3, 5, 7. Prime factorization of 34020 in exponential form is:

34020 = 2² × 3⁵ × 5¹ × 7¹

Step-3: Factors of 34005

List of positive integer factors of 34005 that divides 34005 without a remainder.

1, 3, 5, 15, 2267, 6801, 11335

Step-4: Factors of 34020

List of positive integer factors of 34020 that divides 34005 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 81, 84, 90, 105, 108, 126, 135, 140, 162, 180, 189, 210, 243, 252, 270, 315, 324, 378, 405, 420, 486, 540, 567, 630, 756, 810, 945, 972, 1134, 1215, 1260, 1620, 1701, 1890, 2268, 2430, 2835, 3402, 3780, 4860, 5670, 6804, 8505, 11340, 17010

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34005 and 34020. The biggest common factor number is the GCF number.
So the greatest common factor 34005 and 34020 is 15.

Also check out the Least Common Multiple of 34005 and 34020