What is the Greatest Common Factor of 61200 and 61217?

Greatest common factor (GCF) of 61200 and 61217 is 17.

GCF(61200,61217) = 17

We will now calculate the prime factors of 61200 and 61217, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61200 and 61217.

How to find the GCF of 61200 and 61217?

We will first find the prime factorization of 61200 and 61217. After we will calculate the factors of 61200 and 61217 and find the biggest common factor number .

Step-1: Prime Factorization of 61200

Prime factors of 61200 are 2, 3, 5, 17. Prime factorization of 61200 in exponential form is:

61200 = 2⁴ × 3² × 5² × 17¹

Step-2: Prime Factorization of 61217

Prime factors of 61217 are 13, 17, 277. Prime factorization of 61217 in exponential form is:

61217 = 13¹ × 17¹ × 277¹

Step-3: Factors of 61200

List of positive integer factors of 61200 that divides 61200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 20, 24, 25, 30, 34, 36, 40, 45, 48, 50, 51, 60, 68, 72, 75, 80, 85, 90, 100, 102, 120, 136, 144, 150, 153, 170, 180, 200, 204, 225, 240, 255, 272, 300, 306, 340, 360, 400, 408, 425, 450, 510, 600, 612, 680, 720, 765, 816, 850, 900, 1020, 1200, 1224, 1275, 1360, 1530, 1700, 1800, 2040, 2448, 2550, 3060, 3400, 3600, 3825, 4080, 5100, 6120, 6800, 7650, 10200, 12240, 15300, 20400, 30600

Step-4: Factors of 61217

List of positive integer factors of 61217 that divides 61200 without a remainder.

1, 13, 17, 221, 277, 3601, 4709

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61200 and 61217. The biggest common factor number is the GCF number.
So the greatest common factor 61200 and 61217 is 17.

Also check out the Least Common Multiple of 61200 and 61217