What is the Greatest Common Factor of 75945 and 75960?

Greatest common factor (GCF) of 75945 and 75960 is 15.

GCF(75945,75960) = 15

We will now calculate the prime factors of 75945 and 75960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75945 and 75960.

How to find the GCF of 75945 and 75960?

We will first find the prime factorization of 75945 and 75960. After we will calculate the factors of 75945 and 75960 and find the biggest common factor number .

Step-1: Prime Factorization of 75945

Prime factors of 75945 are 3, 5, 61, 83. Prime factorization of 75945 in exponential form is:

75945 = 3¹ × 5¹ × 61¹ × 83¹

Step-2: Prime Factorization of 75960

Prime factors of 75960 are 2, 3, 5, 211. Prime factorization of 75960 in exponential form is:

75960 = 2³ × 3² × 5¹ × 211¹

Step-3: Factors of 75945

List of positive integer factors of 75945 that divides 75945 without a remainder.

1, 3, 5, 15, 61, 83, 183, 249, 305, 415, 915, 1245, 5063, 15189, 25315

Step-4: Factors of 75960

List of positive integer factors of 75960 that divides 75945 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 211, 360, 422, 633, 844, 1055, 1266, 1688, 1899, 2110, 2532, 3165, 3798, 4220, 5064, 6330, 7596, 8440, 9495, 12660, 15192, 18990, 25320, 37980

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75945 and 75960. The biggest common factor number is the GCF number.
So the greatest common factor 75945 and 75960 is 15.

Also check out the Least Common Multiple of 75945 and 75960