What is the Greatest Common Factor of 74368 and 74382?

Greatest common factor (GCF) of 74368 and 74382 is 14.

GCF(74368,74382) = 14

We will now calculate the prime factors of 74368 and 74382, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74368 and 74382.

How to find the GCF of 74368 and 74382?

We will first find the prime factorization of 74368 and 74382. After we will calculate the factors of 74368 and 74382 and find the biggest common factor number .

Step-1: Prime Factorization of 74368

Prime factors of 74368 are 2, 7, 83. Prime factorization of 74368 in exponential form is:

74368 = 2⁷ × 7¹ × 83¹

Step-2: Prime Factorization of 74382

Prime factors of 74382 are 2, 3, 7, 11, 23. Prime factorization of 74382 in exponential form is:

74382 = 2¹ × 3¹ × 7² × 11¹ × 23¹

Step-3: Factors of 74368

List of positive integer factors of 74368 that divides 74368 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 83, 112, 128, 166, 224, 332, 448, 581, 664, 896, 1162, 1328, 2324, 2656, 4648, 5312, 9296, 10624, 18592, 37184

Step-4: Factors of 74382

List of positive integer factors of 74382 that divides 74368 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 23, 33, 42, 46, 49, 66, 69, 77, 98, 138, 147, 154, 161, 231, 253, 294, 322, 462, 483, 506, 539, 759, 966, 1078, 1127, 1518, 1617, 1771, 2254, 3234, 3381, 3542, 5313, 6762, 10626, 12397, 24794, 37191

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74368 and 74382. The biggest common factor number is the GCF number.
So the greatest common factor 74368 and 74382 is 14.

Also check out the Least Common Multiple of 74368 and 74382