What is the Greatest Common Factor of 61760 and 61776?

Greatest common factor (GCF) of 61760 and 61776 is 16.

GCF(61760,61776) = 16

We will now calculate the prime factors of 61760 and 61776, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 61760 and 61776.

How to find the GCF of 61760 and 61776?

We will first find the prime factorization of 61760 and 61776. After we will calculate the factors of 61760 and 61776 and find the biggest common factor number .

Step-1: Prime Factorization of 61760

Prime factors of 61760 are 2, 5, 193. Prime factorization of 61760 in exponential form is:

61760 = 2⁶ × 5¹ × 193¹

Step-2: Prime Factorization of 61776

Prime factors of 61776 are 2, 3, 11, 13. Prime factorization of 61776 in exponential form is:

61776 = 2⁴ × 3³ × 11¹ × 13¹

Step-3: Factors of 61760

List of positive integer factors of 61760 that divides 61760 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 193, 320, 386, 772, 965, 1544, 1930, 3088, 3860, 6176, 7720, 12352, 15440, 30880

Step-4: Factors of 61776

List of positive integer factors of 61776 that divides 61760 without a remainder.

1, 2, 3, 4, 6, 8, 9, 11, 12, 13, 16, 18, 22, 24, 26, 27, 33, 36, 39, 44, 48, 52, 54, 66, 72, 78, 88, 99, 104, 108, 117, 132, 143, 144, 156, 176, 198, 208, 216, 234, 264, 286, 297, 312, 351, 396, 429, 432, 468, 528, 572, 594, 624, 702, 792, 858, 936, 1144, 1188, 1287, 1404, 1584, 1716, 1872, 2288, 2376, 2574, 2808, 3432, 3861, 4752, 5148, 5616, 6864, 7722, 10296, 15444, 20592, 30888

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 61760 and 61776. The biggest common factor number is the GCF number.
So the greatest common factor 61760 and 61776 is 16.

Also check out the Least Common Multiple of 61760 and 61776