What is the Greatest Common Factor of 75960 and 75978?

Greatest common factor (GCF) of 75960 and 75978 is 18.

GCF(75960,75978) = 18

We will now calculate the prime factors of 75960 and 75978, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75960 and 75978.

How to find the GCF of 75960 and 75978?

We will first find the prime factorization of 75960 and 75978. After we will calculate the factors of 75960 and 75978 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75978

Prime factors of 75978 are 2, 3, 7, 67. Prime factorization of 75978 in exponential form is:

75978 = 2¹ × 3⁴ × 7¹ × 67¹

Step-3: Factors of 75960

List of positive integer factors of 75960 that divides 75960 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

Step-4: Factors of 75978

List of positive integer factors of 75978 that divides 75960 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 67, 81, 126, 134, 162, 189, 201, 378, 402, 469, 567, 603, 938, 1134, 1206, 1407, 1809, 2814, 3618, 4221, 5427, 8442, 10854, 12663, 25326, 37989

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75960 and 75978. The biggest common factor number is the GCF number.
So the greatest common factor 75960 and 75978 is 18.

Also check out the Least Common Multiple of 75960 and 75978