What is the Greatest Common Factor of 34510 and 34524?

Greatest common factor (GCF) of 34510 and 34524 is 14.

GCF(34510,34524) = 14

We will now calculate the prime factors of 34510 and 34524, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34510 and 34524.

How to find the GCF of 34510 and 34524?

We will first find the prime factorization of 34510 and 34524. After we will calculate the factors of 34510 and 34524 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 34524

Prime factors of 34524 are 2, 3, 7, 137. Prime factorization of 34524 in exponential form is:

34524 = 2² × 3² × 7¹ × 137¹

Step-3: Factors of 34510

List of positive integer factors of 34510 that divides 34510 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

Step-4: Factors of 34524

List of positive integer factors of 34524 that divides 34510 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 137, 252, 274, 411, 548, 822, 959, 1233, 1644, 1918, 2466, 2877, 3836, 4932, 5754, 8631, 11508, 17262

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34510 and 34524. The biggest common factor number is the GCF number.
So the greatest common factor 34510 and 34524 is 14.

Also check out the Least Common Multiple of 34510 and 34524