What is the Greatest Common Factor of 75348 and 75366?

Greatest common factor (GCF) of 75348 and 75366 is 18.

GCF(75348,75366) = 18

We will now calculate the prime factors of 75348 and 75366, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75348 and 75366.

How to find the GCF of 75348 and 75366?

We will first find the prime factorization of 75348 and 75366. After we will calculate the factors of 75348 and 75366 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75366

Prime factors of 75366 are 2, 3, 53, 79. Prime factorization of 75366 in exponential form is:

75366 = 2¹ × 3² × 53¹ × 79¹

Step-3: Factors of 75348

List of positive integer factors of 75348 that divides 75348 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

Step-4: Factors of 75366

List of positive integer factors of 75366 that divides 75348 without a remainder.

1, 2, 3, 6, 9, 18, 53, 79, 106, 158, 159, 237, 318, 474, 477, 711, 954, 1422, 4187, 8374, 12561, 25122, 37683

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75348 and 75366. The biggest common factor number is the GCF number.
So the greatest common factor 75348 and 75366 is 18.

Also check out the Least Common Multiple of 75348 and 75366