What is the Greatest Common Factor of 75338 and 75348?

Greatest common factor (GCF) of 75338 and 75348 is 2.

GCF(75338,75348) = 2

We will now calculate the prime factors of 75338 and 75348, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75338 and 75348.

How to find the GCF of 75338 and 75348?

We will first find the prime factorization of 75338 and 75348. After we will calculate the factors of 75338 and 75348 and find the biggest common factor number .

Step-1: Prime Factorization of 75338

Prime factors of 75338 are 2, 139, 271. Prime factorization of 75338 in exponential form is:

75338 = 2¹ × 139¹ × 271¹

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 75338

List of positive integer factors of 75338 that divides 75338 without a remainder.

1, 2, 139, 271, 278, 542, 37669

Step-4: Factors of 75348

List of positive integer factors of 75348 that divides 75338 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 75338 and 75348. The biggest common factor number is the GCF number.
So the greatest common factor 75338 and 75348 is 2.

Also check out the Least Common Multiple of 75338 and 75348