What is the Greatest Common Factor of 34561 and 34580?

Greatest common factor (GCF) of 34561 and 34580 is 19.

GCF(34561,34580) = 19

We will now calculate the prime factors of 34561 and 34580, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34561 and 34580.

How to find the GCF of 34561 and 34580?

We will first find the prime factorization of 34561 and 34580. After we will calculate the factors of 34561 and 34580 and find the biggest common factor number .

Step-1: Prime Factorization of 34561

Prime factors of 34561 are 17, 19, 107. Prime factorization of 34561 in exponential form is:

34561 = 17¹ × 19¹ × 107¹

Step-2: Prime Factorization of 34580

Prime factors of 34580 are 2, 5, 7, 13, 19. Prime factorization of 34580 in exponential form is:

34580 = 2² × 5¹ × 7¹ × 13¹ × 19¹

Step-3: Factors of 34561

List of positive integer factors of 34561 that divides 34561 without a remainder.

1, 17, 19, 107, 323, 1819, 2033

Step-4: Factors of 34580

List of positive integer factors of 34580 that divides 34561 without a remainder.

1, 2, 4, 5, 7, 10, 13, 14, 19, 20, 26, 28, 35, 38, 52, 65, 70, 76, 91, 95, 130, 133, 140, 182, 190, 247, 260, 266, 364, 380, 455, 494, 532, 665, 910, 988, 1235, 1330, 1729, 1820, 2470, 2660, 3458, 4940, 6916, 8645, 17290

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34561 and 34580. The biggest common factor number is the GCF number.
So the greatest common factor 34561 and 34580 is 19.

Also check out the Least Common Multiple of 34561 and 34580