What is the Greatest Common Factor of 29565 and 29580?

Greatest common factor (GCF) of 29565 and 29580 is 15.

GCF(29565,29580) = 15

We will now calculate the prime factors of 29565 and 29580, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29565 and 29580.

How to find the GCF of 29565 and 29580?

We will first find the prime factorization of 29565 and 29580. After we will calculate the factors of 29565 and 29580 and find the biggest common factor number .

Step-1: Prime Factorization of 29565

Prime factors of 29565 are 3, 5, 73. Prime factorization of 29565 in exponential form is:

29565 = 3⁴ × 5¹ × 73¹

Step-2: Prime Factorization of 29580

Prime factors of 29580 are 2, 3, 5, 17, 29. Prime factorization of 29580 in exponential form is:

29580 = 2² × 3¹ × 5¹ × 17¹ × 29¹

Step-3: Factors of 29565

List of positive integer factors of 29565 that divides 29565 without a remainder.

1, 3, 5, 9, 15, 27, 45, 73, 81, 135, 219, 365, 405, 657, 1095, 1971, 3285, 5913, 9855

Step-4: Factors of 29580

List of positive integer factors of 29580 that divides 29565 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 29, 30, 34, 51, 58, 60, 68, 85, 87, 102, 116, 145, 170, 174, 204, 255, 290, 340, 348, 435, 493, 510, 580, 870, 986, 1020, 1479, 1740, 1972, 2465, 2958, 4930, 5916, 7395, 9860, 14790

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29565 and 29580. The biggest common factor number is the GCF number.
So the greatest common factor 29565 and 29580 is 15.

Also check out the Least Common Multiple of 29565 and 29580