What is the Greatest Common Factor of 74384 and 74400?

Greatest common factor (GCF) of 74384 and 74400 is 16.

GCF(74384,74400) = 16

We will now calculate the prime factors of 74384 and 74400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74384 and 74400.

How to find the GCF of 74384 and 74400?

We will first find the prime factorization of 74384 and 74400. After we will calculate the factors of 74384 and 74400 and find the biggest common factor number .

Step-1: Prime Factorization of 74384

Prime factors of 74384 are 2, 4649. Prime factorization of 74384 in exponential form is:

74384 = 2⁴ × 4649¹

Step-2: 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-3: Factors of 74384

List of positive integer factors of 74384 that divides 74384 without a remainder.

1, 2, 4, 8, 16, 4649, 9298, 18596, 37192

Step-4: Factors of 74400

List of positive integer factors of 74400 that divides 74384 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74384 and 74400. The biggest common factor number is the GCF number.
So the greatest common factor 74384 and 74400 is 16.

Also check out the Least Common Multiple of 74384 and 74400