What is the Greatest Common Factor of 74400 and 74420?

Greatest common factor (GCF) of 74400 and 74420 is 20.

GCF(74400,74420) = 20

We will now calculate the prime factors of 74400 and 74420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 74400 and 74420.

How to find the GCF of 74400 and 74420?

We will first find the prime factorization of 74400 and 74420. After we will calculate the factors of 74400 and 74420 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 74420

Prime factors of 74420 are 2, 5, 61. Prime factorization of 74420 in exponential form is:

74420 = 2² × 5¹ × 61²

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 74420

List of positive integer factors of 74420 that divides 74400 without a remainder.

1, 2, 4, 5, 10, 20, 61, 122, 244, 305, 610, 1220, 3721, 7442, 14884, 18605, 37210

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 74400 and 74420. The biggest common factor number is the GCF number.
So the greatest common factor 74400 and 74420 is 20.

Also check out the Least Common Multiple of 74400 and 74420