What is the Greatest Common Factor of 75905 and 75922?

Greatest common factor (GCF) of 75905 and 75922 is 17.

GCF(75905,75922) = 17

We will now calculate the prime factors of 75905 and 75922, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75905 and 75922.

How to find the GCF of 75905 and 75922?

We will first find the prime factorization of 75905 and 75922. After we will calculate the factors of 75905 and 75922 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 75922

Prime factors of 75922 are 2, 7, 11, 17, 29. Prime factorization of 75922 in exponential form is:

75922 = 2¹ × 7¹ × 11¹ × 17¹ × 29¹

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 75922

List of positive integer factors of 75922 that divides 75905 without a remainder.

1, 2, 7, 11, 14, 17, 22, 29, 34, 58, 77, 119, 154, 187, 203, 238, 319, 374, 406, 493, 638, 986, 1309, 2233, 2618, 3451, 4466, 5423, 6902, 10846, 37961

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75905 and 75922. The biggest common factor number is the GCF number.
So the greatest common factor 75905 and 75922 is 17.

Also check out the Least Common Multiple of 75905 and 75922