What is the Greatest Common Factor of 61200 and 61216?

Greatest common factor (GCF) of 61200 and 61216 is 16.

GCF(61200,61216) = 16

We will now calculate the prime factors of 61200 and 61216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61200 and 61216.

How to find the GCF of 61200 and 61216?

We will first find the prime factorization of 61200 and 61216. After we will calculate the factors of 61200 and 61216 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 61216

Prime factors of 61216 are 2, 1913. Prime factorization of 61216 in exponential form is:

61216 = 2⁵ × 1913¹

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 61216

List of positive integer factors of 61216 that divides 61200 without a remainder.

1, 2, 4, 8, 16, 32, 1913, 3826, 7652, 15304, 30608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61200 and 61216. The biggest common factor number is the GCF number.
So the greatest common factor 61200 and 61216 is 16.

Also check out the Least Common Multiple of 61200 and 61216