What is the Greatest Common Factor of 75334 and 75348?

Greatest common factor (GCF) of 75334 and 75348 is 14.

GCF(75334,75348) = 14

We will now calculate the prime factors of 75334 and 75348, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75334 and 75348.

How to find the GCF of 75334 and 75348?

We will first find the prime factorization of 75334 and 75348. After we will calculate the factors of 75334 and 75348 and find the biggest common factor number .

Step-1: Prime Factorization of 75334

Prime factors of 75334 are 2, 7, 5381. Prime factorization of 75334 in exponential form is:

75334 = 2¹ × 7¹ × 5381¹

Step-2: Prime Factorization of 75348

Prime factors of 75348 are 2, 3, 7, 13, 23. Prime factorization of 75348 in exponential form is:

75348 = 2² × 3² × 7¹ × 13¹ × 23¹

Step-3: Factors of 75334

List of positive integer factors of 75334 that divides 75334 without a remainder.

1, 2, 7, 14, 5381, 10762, 37667

Step-4: Factors of 75348

List of positive integer factors of 75348 that divides 75334 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 13, 14, 18, 21, 23, 26, 28, 36, 39, 42, 46, 52, 63, 69, 78, 84, 91, 92, 117, 126, 138, 156, 161, 182, 207, 234, 252, 273, 276, 299, 322, 364, 414, 468, 483, 546, 598, 644, 819, 828, 897, 966, 1092, 1196, 1449, 1638, 1794, 1932, 2093, 2691, 2898, 3276, 3588, 4186, 5382, 5796, 6279, 8372, 10764, 12558, 18837, 25116, 37674

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75334 and 75348. The biggest common factor number is the GCF number.
So the greatest common factor 75334 and 75348 is 14.

Also check out the Least Common Multiple of 75334 and 75348