What is the Greatest Common Factor of 61593 and 61600?

Greatest common factor (GCF) of 61593 and 61600 is 7.

GCF(61593,61600) = 7

We will now calculate the prime factors of 61593 and 61600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61593 and 61600.

How to find the GCF of 61593 and 61600?

We will first find the prime factorization of 61593 and 61600. After we will calculate the factors of 61593 and 61600 and find the biggest common factor number .

Step-1: Prime Factorization of 61593

Prime factors of 61593 are 3, 7, 419. Prime factorization of 61593 in exponential form is:

61593 = 3¹ × 7² × 419¹

Step-2: Prime Factorization of 61600

Prime factors of 61600 are 2, 5, 7, 11. Prime factorization of 61600 in exponential form is:

61600 = 2⁵ × 5² × 7¹ × 11¹

Step-3: Factors of 61593

List of positive integer factors of 61593 that divides 61593 without a remainder.

1, 3, 7, 21, 49, 147, 419, 1257, 2933, 8799, 20531

Step-4: Factors of 61600

List of positive integer factors of 61600 that divides 61593 without a remainder.

1, 2, 4, 5, 7, 8, 10, 11, 14, 16, 20, 22, 25, 28, 32, 35, 40, 44, 50, 55, 56, 70, 77, 80, 88, 100, 110, 112, 140, 154, 160, 175, 176, 200, 220, 224, 275, 280, 308, 350, 352, 385, 400, 440, 550, 560, 616, 700, 770, 800, 880, 1100, 1120, 1232, 1400, 1540, 1760, 1925, 2200, 2464, 2800, 3080, 3850, 4400, 5600, 6160, 7700, 8800, 12320, 15400, 30800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61593 and 61600. The biggest common factor number is the GCF number.
So the greatest common factor 61593 and 61600 is 7.

Also check out the Least Common Multiple of 61593 and 61600