What is the Greatest Common Factor of 89743 and 89760?

Greatest common factor (GCF) of 89743 and 89760 is 17.

GCF(89743,89760) = 17

We will now calculate the prime factors of 89743 and 89760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 89743 and 89760.

How to find the GCF of 89743 and 89760?

We will first find the prime factorization of 89743 and 89760. After we will calculate the factors of 89743 and 89760 and find the biggest common factor number .

Step-1: Prime Factorization of 89743

Prime factors of 89743 are 17, 5279. Prime factorization of 89743 in exponential form is:

89743 = 17¹ × 5279¹

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 89743

List of positive integer factors of 89743 that divides 89743 without a remainder.

1, 17, 5279

Step-4: Factors of 89760

List of positive integer factors of 89760 that divides 89743 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 89743 and 89760. The biggest common factor number is the GCF number.
So the greatest common factor 89743 and 89760 is 17.

Also check out the Least Common Multiple of 89743 and 89760