What is the Greatest Common Factor of 75614 and 75628?

Greatest common factor (GCF) of 75614 and 75628 is 14.

GCF(75614,75628) = 14

We will now calculate the prime factors of 75614 and 75628, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75614 and 75628.

How to find the GCF of 75614 and 75628?

We will first find the prime factorization of 75614 and 75628. After we will calculate the factors of 75614 and 75628 and find the biggest common factor number .

Step-1: Prime Factorization of 75614

Prime factors of 75614 are 2, 7, 11, 491. Prime factorization of 75614 in exponential form is:

75614 = 2¹ × 7¹ × 11¹ × 491¹

Step-2: Prime Factorization of 75628

Prime factors of 75628 are 2, 7, 37, 73. Prime factorization of 75628 in exponential form is:

75628 = 2² × 7¹ × 37¹ × 73¹

Step-3: Factors of 75614

List of positive integer factors of 75614 that divides 75614 without a remainder.

1, 2, 7, 11, 14, 22, 77, 154, 491, 982, 3437, 5401, 6874, 10802, 37807

Step-4: Factors of 75628

List of positive integer factors of 75628 that divides 75614 without a remainder.

1, 2, 4, 7, 14, 28, 37, 73, 74, 146, 148, 259, 292, 511, 518, 1022, 1036, 2044, 2701, 5402, 10804, 18907, 37814

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75614 and 75628. The biggest common factor number is the GCF number.
So the greatest common factor 75614 and 75628 is 14.

Also check out the Least Common Multiple of 75614 and 75628