What is the Greatest Common Factor of 89749 and 89760?

Greatest common factor (GCF) of 89749 and 89760 is 11.

GCF(89749,89760) = 11

We will now calculate the prime factors of 89749 and 89760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 89749 and 89760.

How to find the GCF of 89749 and 89760?

We will first find the prime factorization of 89749 and 89760. After we will calculate the factors of 89749 and 89760 and find the biggest common factor number .

Step-1: Prime Factorization of 89749

Prime factors of 89749 are 11, 41, 199. Prime factorization of 89749 in exponential form is:

89749 = 11¹ × 41¹ × 199¹

Step-2: Prime Factorization of 89760

Prime factors of 89760 are 2, 3, 5, 11, 17. Prime factorization of 89760 in exponential form is:

89760 = 2⁵ × 3¹ × 5¹ × 11¹ × 17¹

Step-3: Factors of 89749

List of positive integer factors of 89749 that divides 89749 without a remainder.

1, 11, 41, 199, 451, 2189, 8159

Step-4: Factors of 89760

List of positive integer factors of 89760 that divides 89749 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 17, 20, 22, 24, 30, 32, 33, 34, 40, 44, 48, 51, 55, 60, 66, 68, 80, 85, 88, 96, 102, 110, 120, 132, 136, 160, 165, 170, 176, 187, 204, 220, 240, 255, 264, 272, 330, 340, 352, 374, 408, 440, 480, 510, 528, 544, 561, 660, 680, 748, 816, 880, 935, 1020, 1056, 1122, 1320, 1360, 1496, 1632, 1760, 1870, 2040, 2244, 2640, 2720, 2805, 2992, 3740, 4080, 4488, 5280, 5610, 5984, 7480, 8160, 8976, 11220, 14960, 17952, 22440, 29920, 44880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 89749 and 89760. The biggest common factor number is the GCF number.
So the greatest common factor 89749 and 89760 is 11.

Also check out the Least Common Multiple of 89749 and 89760