What is the Greatest Common Factor of 74400 and 74412?

Greatest common factor (GCF) of 74400 and 74412 is 12.

GCF(74400,74412) = 12

We will now calculate the prime factors of 74400 and 74412, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74400 and 74412.

How to find the GCF of 74400 and 74412?

We will first find the prime factorization of 74400 and 74412. After we will calculate the factors of 74400 and 74412 and find the biggest common factor number .

Step-1: Prime Factorization of 74400

Prime factors of 74400 are 2, 3, 5, 31. Prime factorization of 74400 in exponential form is:

74400 = 2⁵ × 3¹ × 5² × 31¹

Step-2: Prime Factorization of 74412

Prime factors of 74412 are 2, 3, 13, 53. Prime factorization of 74412 in exponential form is:

74412 = 2² × 3³ × 13¹ × 53¹

Step-3: Factors of 74400

List of positive integer factors of 74400 that divides 74400 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 31, 32, 40, 48, 50, 60, 62, 75, 80, 93, 96, 100, 120, 124, 150, 155, 160, 186, 200, 240, 248, 300, 310, 372, 400, 465, 480, 496, 600, 620, 744, 775, 800, 930, 992, 1200, 1240, 1488, 1550, 1860, 2325, 2400, 2480, 2976, 3100, 3720, 4650, 4960, 6200, 7440, 9300, 12400, 14880, 18600, 24800, 37200

Step-4: Factors of 74412

List of positive integer factors of 74412 that divides 74400 without a remainder.

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 52, 53, 54, 78, 106, 108, 117, 156, 159, 212, 234, 318, 351, 468, 477, 636, 689, 702, 954, 1378, 1404, 1431, 1908, 2067, 2756, 2862, 4134, 5724, 6201, 8268, 12402, 18603, 24804, 37206

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74400 and 74412. The biggest common factor number is the GCF number.
So the greatest common factor 74400 and 74412 is 12.

Also check out the Least Common Multiple of 74400 and 74412