What is the Greatest Common Factor of 34500 and 34510?

Greatest common factor (GCF) of 34500 and 34510 is 10.

GCF(34500,34510) = 10

We will now calculate the prime factors of 34500 and 34510, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34500 and 34510.

How to find the GCF of 34500 and 34510?

We will first find the prime factorization of 34500 and 34510. After we will calculate the factors of 34500 and 34510 and find the biggest common factor number .

Step-1: Prime Factorization of 34500

Prime factors of 34500 are 2, 3, 5, 23. Prime factorization of 34500 in exponential form is:

34500 = 2² × 3¹ × 5³ × 23¹

Step-2: Prime Factorization of 34510

Prime factors of 34510 are 2, 5, 7, 17, 29. Prime factorization of 34510 in exponential form is:

34510 = 2¹ × 5¹ × 7¹ × 17¹ × 29¹

Step-3: Factors of 34500

List of positive integer factors of 34500 that divides 34500 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 25, 30, 46, 50, 60, 69, 75, 92, 100, 115, 125, 138, 150, 230, 250, 276, 300, 345, 375, 460, 500, 575, 690, 750, 1150, 1380, 1500, 1725, 2300, 2875, 3450, 5750, 6900, 8625, 11500, 17250

Step-4: Factors of 34510

List of positive integer factors of 34510 that divides 34500 without a remainder.

1, 2, 5, 7, 10, 14, 17, 29, 34, 35, 58, 70, 85, 119, 145, 170, 203, 238, 290, 406, 493, 595, 986, 1015, 1190, 2030, 2465, 3451, 4930, 6902, 17255

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34500 and 34510. The biggest common factor number is the GCF number.
So the greatest common factor 34500 and 34510 is 10.

Also check out the Least Common Multiple of 34500 and 34510