What is the Greatest Common Factor of 34090 and 34100?

Greatest common factor (GCF) of 34090 and 34100 is 10.

GCF(34090,34100) = 10

We will now calculate the prime factors of 34090 and 34100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34090 and 34100.

How to find the GCF of 34090 and 34100?

We will first find the prime factorization of 34090 and 34100. After we will calculate the factors of 34090 and 34100 and find the biggest common factor number .

Step-1: Prime Factorization of 34090

Prime factors of 34090 are 2, 5, 7, 487. Prime factorization of 34090 in exponential form is:

34090 = 2¹ × 5¹ × 7¹ × 487¹

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 34090

List of positive integer factors of 34090 that divides 34090 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 487, 974, 2435, 3409, 4870, 6818, 17045

Step-4: Factors of 34100

List of positive integer factors of 34100 that divides 34090 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 34090 and 34100. The biggest common factor number is the GCF number.
So the greatest common factor 34090 and 34100 is 10.

Also check out the Least Common Multiple of 34090 and 34100