What is the Greatest Common Factor of 85905 and 85920?

Greatest common factor (GCF) of 85905 and 85920 is 15.

GCF(85905,85920) = 15

We will now calculate the prime factors of 85905 and 85920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 85905 and 85920.

How to find the GCF of 85905 and 85920?

We will first find the prime factorization of 85905 and 85920. After we will calculate the factors of 85905 and 85920 and find the biggest common factor number .

Step-1: Prime Factorization of 85905

Prime factors of 85905 are 3, 5, 23, 83. Prime factorization of 85905 in exponential form is:

85905 = 3² × 5¹ × 23¹ × 83¹

Step-2: Prime Factorization of 85920

Prime factors of 85920 are 2, 3, 5, 179. Prime factorization of 85920 in exponential form is:

85920 = 2⁵ × 3¹ × 5¹ × 179¹

Step-3: Factors of 85905

List of positive integer factors of 85905 that divides 85905 without a remainder.

1, 3, 5, 9, 15, 23, 45, 69, 83, 115, 207, 249, 345, 415, 747, 1035, 1245, 1909, 3735, 5727, 9545, 17181, 28635

Step-4: Factors of 85920

List of positive integer factors of 85920 that divides 85905 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 179, 240, 358, 480, 537, 716, 895, 1074, 1432, 1790, 2148, 2685, 2864, 3580, 4296, 5370, 5728, 7160, 8592, 10740, 14320, 17184, 21480, 28640, 42960

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 85905 and 85920. The biggest common factor number is the GCF number.
So the greatest common factor 85905 and 85920 is 15.

Also check out the Least Common Multiple of 85905 and 85920