What is the Greatest Common Factor of 75905 and 75920?

Greatest common factor (GCF) of 75905 and 75920 is 5.

GCF(75905,75920) = 5

We will now calculate the prime factors of 75905 and 75920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75905 and 75920.

How to find the GCF of 75905 and 75920?

We will first find the prime factorization of 75905 and 75920. After we will calculate the factors of 75905 and 75920 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 75920

Prime factors of 75920 are 2, 5, 13, 73. Prime factorization of 75920 in exponential form is:

75920 = 2⁴ × 5¹ × 13¹ × 73¹

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 75920

List of positive integer factors of 75920 that divides 75905 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 26, 40, 52, 65, 73, 80, 104, 130, 146, 208, 260, 292, 365, 520, 584, 730, 949, 1040, 1168, 1460, 1898, 2920, 3796, 4745, 5840, 7592, 9490, 15184, 18980, 37960

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75905 and 75920. The biggest common factor number is the GCF number.
So the greatest common factor 75905 and 75920 is 5.

Also check out the Least Common Multiple of 75905 and 75920