What is the Greatest Common Factor of 89760 and 89765?

Greatest common factor (GCF) of 89760 and 89765 is 5.

GCF(89760,89765) = 5

We will now calculate the prime factors of 89760 and 89765, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 89760 and 89765.

How to find the GCF of 89760 and 89765?

We will first find the prime factorization of 89760 and 89765. After we will calculate the factors of 89760 and 89765 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 89765

Prime factors of 89765 are 5, 13, 1381. Prime factorization of 89765 in exponential form is:

89765 = 5¹ × 13¹ × 1381¹

Step-3: Factors of 89760

List of positive integer factors of 89760 that divides 89760 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

Step-4: Factors of 89765

List of positive integer factors of 89765 that divides 89760 without a remainder.

1, 5, 13, 65, 1381, 6905, 17953

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 89760 and 89765. The biggest common factor number is the GCF number.
So the greatest common factor 89760 and 89765 is 5.

Also check out the Least Common Multiple of 89760 and 89765