What is the Greatest Common Factor of 75866 and 75880?

Greatest common factor (GCF) of 75866 and 75880 is 14.

GCF(75866,75880) = 14

We will now calculate the prime factors of 75866 and 75880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75866 and 75880.

How to find the GCF of 75866 and 75880?

We will first find the prime factorization of 75866 and 75880. After we will calculate the factors of 75866 and 75880 and find the biggest common factor number .

Step-1: Prime Factorization of 75866

Prime factors of 75866 are 2, 7, 5419. Prime factorization of 75866 in exponential form is:

75866 = 2¹ × 7¹ × 5419¹

Step-2: Prime Factorization of 75880

Prime factors of 75880 are 2, 5, 7, 271. Prime factorization of 75880 in exponential form is:

75880 = 2³ × 5¹ × 7¹ × 271¹

Step-3: Factors of 75866

List of positive integer factors of 75866 that divides 75866 without a remainder.

1, 2, 7, 14, 5419, 10838, 37933

Step-4: Factors of 75880

List of positive integer factors of 75880 that divides 75866 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 271, 280, 542, 1084, 1355, 1897, 2168, 2710, 3794, 5420, 7588, 9485, 10840, 15176, 18970, 37940

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75866 and 75880. The biggest common factor number is the GCF number.
So the greatest common factor 75866 and 75880 is 14.

Also check out the Least Common Multiple of 75866 and 75880