What is the Greatest Common Factor of 75905 and 75924?

Greatest common factor (GCF) of 75905 and 75924 is 19.

GCF(75905,75924) = 19

We will now calculate the prime factors of 75905 and 75924, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75905 and 75924.

How to find the GCF of 75905 and 75924?

We will first find the prime factorization of 75905 and 75924. After we will calculate the factors of 75905 and 75924 and find the biggest common factor number .

Step-1: Prime Factorization of 75905

Prime factors of 75905 are 5, 17, 19, 47. Prime factorization of 75905 in exponential form is:

75905 = 5¹ × 17¹ × 19¹ × 47¹

Step-2: Prime Factorization of 75924

Prime factors of 75924 are 2, 3, 19, 37. Prime factorization of 75924 in exponential form is:

75924 = 2² × 3³ × 19¹ × 37¹

Step-3: Factors of 75905

List of positive integer factors of 75905 that divides 75905 without a remainder.

1, 5, 17, 19, 47, 85, 95, 235, 323, 799, 893, 1615, 3995, 4465, 15181

Step-4: Factors of 75924

List of positive integer factors of 75924 that divides 75905 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 19, 27, 36, 37, 38, 54, 57, 74, 76, 108, 111, 114, 148, 171, 222, 228, 333, 342, 444, 513, 666, 684, 703, 999, 1026, 1332, 1406, 1998, 2052, 2109, 2812, 3996, 4218, 6327, 8436, 12654, 18981, 25308, 37962

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75905 and 75924. The biggest common factor number is the GCF number.
So the greatest common factor 75905 and 75924 is 19.

Also check out the Least Common Multiple of 75905 and 75924