What is the Greatest Common Factor of 34580 and 34600?

Greatest common factor (GCF) of 34580 and 34600 is 20.

GCF(34580,34600) = 20

We will now calculate the prime factors of 34580 and 34600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34580 and 34600.

How to find the GCF of 34580 and 34600?

We will first find the prime factorization of 34580 and 34600. After we will calculate the factors of 34580 and 34600 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 34600

Prime factors of 34600 are 2, 5, 173. Prime factorization of 34600 in exponential form is:

34600 = 2³ × 5² × 173¹

Step-3: Factors of 34580

List of positive integer factors of 34580 that divides 34580 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

Step-4: Factors of 34600

List of positive integer factors of 34600 that divides 34580 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 173, 200, 346, 692, 865, 1384, 1730, 3460, 4325, 6920, 8650, 17300

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34580 and 34600. The biggest common factor number is the GCF number.
So the greatest common factor 34580 and 34600 is 20.

Also check out the Least Common Multiple of 34580 and 34600