What is the Greatest Common Factor of 75838 and 75852?

Greatest common factor (GCF) of 75838 and 75852 is 14.

GCF(75838,75852) = 14

We will now calculate the prime factors of 75838 and 75852, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75838 and 75852.

How to find the GCF of 75838 and 75852?

We will first find the prime factorization of 75838 and 75852. After we will calculate the factors of 75838 and 75852 and find the biggest common factor number .

Step-1: Prime Factorization of 75838

Prime factors of 75838 are 2, 7, 5417. Prime factorization of 75838 in exponential form is:

75838 = 2¹ × 7¹ × 5417¹

Step-2: Prime Factorization of 75852

Prime factors of 75852 are 2, 3, 7, 43. Prime factorization of 75852 in exponential form is:

75852 = 2² × 3² × 7² × 43¹

Step-3: Factors of 75838

List of positive integer factors of 75838 that divides 75838 without a remainder.

1, 2, 7, 14, 5417, 10834, 37919

Step-4: Factors of 75852

List of positive integer factors of 75852 that divides 75838 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 43, 49, 63, 84, 86, 98, 126, 129, 147, 172, 196, 252, 258, 294, 301, 387, 441, 516, 588, 602, 774, 882, 903, 1204, 1548, 1764, 1806, 2107, 2709, 3612, 4214, 5418, 6321, 8428, 10836, 12642, 18963, 25284, 37926

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75838 and 75852. The biggest common factor number is the GCF number.
So the greatest common factor 75838 and 75852 is 14.

Also check out the Least Common Multiple of 75838 and 75852