What is the Greatest Common Factor of 74340 and 74360?

Greatest common factor (GCF) of 74340 and 74360 is 20.

GCF(74340,74360) = 20

We will now calculate the prime factors of 74340 and 74360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74340 and 74360.

How to find the GCF of 74340 and 74360?

We will first find the prime factorization of 74340 and 74360. After we will calculate the factors of 74340 and 74360 and find the biggest common factor number .

Step-1: Prime Factorization of 74340

Prime factors of 74340 are 2, 3, 5, 7, 59. Prime factorization of 74340 in exponential form is:

74340 = 2² × 3² × 5¹ × 7¹ × 59¹

Step-2: Prime Factorization of 74360

Prime factors of 74360 are 2, 5, 11, 13. Prime factorization of 74360 in exponential form is:

74360 = 2³ × 5¹ × 11¹ × 13²

Step-3: Factors of 74340

List of positive integer factors of 74340 that divides 74340 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 59, 60, 63, 70, 84, 90, 105, 118, 126, 140, 177, 180, 210, 236, 252, 295, 315, 354, 413, 420, 531, 590, 630, 708, 826, 885, 1062, 1180, 1239, 1260, 1652, 1770, 2065, 2124, 2478, 2655, 3540, 3717, 4130, 4956, 5310, 6195, 7434, 8260, 10620, 12390, 14868, 18585, 24780, 37170

Step-4: Factors of 74360

List of positive integer factors of 74360 that divides 74340 without a remainder.

1, 2, 4, 5, 8, 10, 11, 13, 20, 22, 26, 40, 44, 52, 55, 65, 88, 104, 110, 130, 143, 169, 220, 260, 286, 338, 440, 520, 572, 676, 715, 845, 1144, 1352, 1430, 1690, 1859, 2860, 3380, 3718, 5720, 6760, 7436, 9295, 14872, 18590, 37180

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74340 and 74360. The biggest common factor number is the GCF number.
So the greatest common factor 74340 and 74360 is 20.

Also check out the Least Common Multiple of 74340 and 74360