What is the Greatest Common Factor of 89760 and 89772?

Greatest common factor (GCF) of 89760 and 89772 is 12.

GCF(89760,89772) = 12

We will now calculate the prime factors of 89760 and 89772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 89760 and 89772.

How to find the GCF of 89760 and 89772?

We will first find the prime factorization of 89760 and 89772. After we will calculate the factors of 89760 and 89772 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 89772

Prime factors of 89772 are 2, 3, 7481. Prime factorization of 89772 in exponential form is:

89772 = 2² × 3¹ × 7481¹

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 89772

List of positive integer factors of 89772 that divides 89760 without a remainder.

1, 2, 3, 4, 6, 12, 7481, 14962, 22443, 29924, 44886

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 89760 and 89772. The biggest common factor number is the GCF number.
So the greatest common factor 89760 and 89772 is 12.

Also check out the Least Common Multiple of 89760 and 89772