What is the Greatest Common Factor of 34085 and 34100?

Greatest common factor (GCF) of 34085 and 34100 is 5.

GCF(34085,34100) = 5

We will now calculate the prime factors of 34085 and 34100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34085 and 34100.

How to find the GCF of 34085 and 34100?

We will first find the prime factorization of 34085 and 34100. After we will calculate the factors of 34085 and 34100 and find the biggest common factor number .

Step-1: Prime Factorization of 34085

Prime factors of 34085 are 5, 17, 401. Prime factorization of 34085 in exponential form is:

34085 = 5¹ × 17¹ × 401¹

Step-2: Prime Factorization of 34100

Prime factors of 34100 are 2, 5, 11, 31. Prime factorization of 34100 in exponential form is:

34100 = 2² × 5² × 11¹ × 31¹

Step-3: Factors of 34085

List of positive integer factors of 34085 that divides 34085 without a remainder.

1, 5, 17, 85, 401, 2005, 6817

Step-4: Factors of 34100

List of positive integer factors of 34100 that divides 34085 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 25, 31, 44, 50, 55, 62, 100, 110, 124, 155, 220, 275, 310, 341, 550, 620, 682, 775, 1100, 1364, 1550, 1705, 3100, 3410, 6820, 8525, 17050

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34085 and 34100. The biggest common factor number is the GCF number.
So the greatest common factor 34085 and 34100 is 5.

Also check out the Least Common Multiple of 34085 and 34100