What is the Greatest Common Factor of 90400 and 90420?

Greatest common factor (GCF) of 90400 and 90420 is 20.

GCF(90400,90420) = 20

We will now calculate the prime factors of 90400 and 90420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 90400 and 90420.

How to find the GCF of 90400 and 90420?

We will first find the prime factorization of 90400 and 90420. After we will calculate the factors of 90400 and 90420 and find the biggest common factor number .

Step-1: Prime Factorization of 90400

Prime factors of 90400 are 2, 5, 113. Prime factorization of 90400 in exponential form is:

90400 = 2⁵ × 5² × 113¹

Step-2: Prime Factorization of 90420

Prime factors of 90420 are 2, 3, 5, 11, 137. Prime factorization of 90420 in exponential form is:

90420 = 2² × 3¹ × 5¹ × 11¹ × 137¹

Step-3: Factors of 90400

List of positive integer factors of 90400 that divides 90400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 113, 160, 200, 226, 400, 452, 565, 800, 904, 1130, 1808, 2260, 2825, 3616, 4520, 5650, 9040, 11300, 18080, 22600, 45200

Step-4: Factors of 90420

List of positive integer factors of 90420 that divides 90400 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 137, 165, 220, 274, 330, 411, 548, 660, 685, 822, 1370, 1507, 1644, 2055, 2740, 3014, 4110, 4521, 6028, 7535, 8220, 9042, 15070, 18084, 22605, 30140, 45210

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 90400 and 90420. The biggest common factor number is the GCF number.
So the greatest common factor 90400 and 90420 is 20.

Also check out the Least Common Multiple of 90400 and 90420