What is the Greatest Common Factor of 29580 and 29600?

Greatest common factor (GCF) of 29580 and 29600 is 20.

GCF(29580,29600) = 20

We will now calculate the prime factors of 29580 and 29600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29580 and 29600.

How to find the GCF of 29580 and 29600?

We will first find the prime factorization of 29580 and 29600. After we will calculate the factors of 29580 and 29600 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 29600

Prime factors of 29600 are 2, 5, 37. Prime factorization of 29600 in exponential form is:

29600 = 2⁵ × 5² × 37¹

Step-3: Factors of 29580

List of positive integer factors of 29580 that divides 29580 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

Step-4: Factors of 29600

List of positive integer factors of 29600 that divides 29580 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 37, 40, 50, 74, 80, 100, 148, 160, 185, 200, 296, 370, 400, 592, 740, 800, 925, 1184, 1480, 1850, 2960, 3700, 5920, 7400, 14800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29580 and 29600. The biggest common factor number is the GCF number.
So the greatest common factor 29580 and 29600 is 20.

Also check out the Least Common Multiple of 29580 and 29600