What is the Greatest Common Factor of 29500 and 29520?

Greatest common factor (GCF) of 29500 and 29520 is 20.

GCF(29500,29520) = 20

We will now calculate the prime factors of 29500 and 29520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 29500 and 29520.

How to find the GCF of 29500 and 29520?

We will first find the prime factorization of 29500 and 29520. After we will calculate the factors of 29500 and 29520 and find the biggest common factor number .

Step-1: Prime Factorization of 29500

Prime factors of 29500 are 2, 5, 59. Prime factorization of 29500 in exponential form is:

29500 = 2² × 5³ × 59¹

Step-2: Prime Factorization of 29520

Prime factors of 29520 are 2, 3, 5, 41. Prime factorization of 29520 in exponential form is:

29520 = 2⁴ × 3² × 5¹ × 41¹

Step-3: Factors of 29500

List of positive integer factors of 29500 that divides 29500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 59, 100, 118, 125, 236, 250, 295, 500, 590, 1180, 1475, 2950, 5900, 7375, 14750

Step-4: Factors of 29520

List of positive integer factors of 29520 that divides 29500 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 41, 45, 48, 60, 72, 80, 82, 90, 120, 123, 144, 164, 180, 205, 240, 246, 328, 360, 369, 410, 492, 615, 656, 720, 738, 820, 984, 1230, 1476, 1640, 1845, 1968, 2460, 2952, 3280, 3690, 4920, 5904, 7380, 9840, 14760

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 29500 and 29520. The biggest common factor number is the GCF number.
So the greatest common factor 29500 and 29520 is 20.

Also check out the Least Common Multiple of 29500 and 29520