What is the Greatest Common Factor of 75985 and 75992?

Greatest common factor (GCF) of 75985 and 75992 is 7.

GCF(75985,75992) = 7

We will now calculate the prime factors of 75985 and 75992, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75985 and 75992.

How to find the GCF of 75985 and 75992?

We will first find the prime factorization of 75985 and 75992. After we will calculate the factors of 75985 and 75992 and find the biggest common factor number .

Step-1: Prime Factorization of 75985

Prime factors of 75985 are 5, 7, 13, 167. Prime factorization of 75985 in exponential form is:

75985 = 5¹ × 7¹ × 13¹ × 167¹

Step-2: Prime Factorization of 75992

Prime factors of 75992 are 2, 7, 23, 59. Prime factorization of 75992 in exponential form is:

75992 = 2³ × 7¹ × 23¹ × 59¹

Step-3: Factors of 75985

List of positive integer factors of 75985 that divides 75985 without a remainder.

1, 5, 7, 13, 35, 65, 91, 167, 455, 835, 1169, 2171, 5845, 10855, 15197

Step-4: Factors of 75992

List of positive integer factors of 75992 that divides 75985 without a remainder.

1, 2, 4, 7, 8, 14, 23, 28, 46, 56, 59, 92, 118, 161, 184, 236, 322, 413, 472, 644, 826, 1288, 1357, 1652, 2714, 3304, 5428, 9499, 10856, 18998, 37996

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75985 and 75992. The biggest common factor number is the GCF number.
So the greatest common factor 75985 and 75992 is 7.

Also check out the Least Common Multiple of 75985 and 75992