What is the Greatest Common Factor of 90480 and 90500?

Greatest common factor (GCF) of 90480 and 90500 is 20.

GCF(90480,90500) = 20

We will now calculate the prime factors of 90480 and 90500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 90480 and 90500.

How to find the GCF of 90480 and 90500?

We will first find the prime factorization of 90480 and 90500. After we will calculate the factors of 90480 and 90500 and find the biggest common factor number .

Step-1: Prime Factorization of 90480

Prime factors of 90480 are 2, 3, 5, 13, 29. Prime factorization of 90480 in exponential form is:

90480 = 2⁴ × 3¹ × 5¹ × 13¹ × 29¹

Step-2: Prime Factorization of 90500

Prime factors of 90500 are 2, 5, 181. Prime factorization of 90500 in exponential form is:

90500 = 2² × 5³ × 181¹

Step-3: Factors of 90480

List of positive integer factors of 90480 that divides 90480 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 16, 20, 24, 26, 29, 30, 39, 40, 48, 52, 58, 60, 65, 78, 80, 87, 104, 116, 120, 130, 145, 156, 174, 195, 208, 232, 240, 260, 290, 312, 348, 377, 390, 435, 464, 520, 580, 624, 696, 754, 780, 870, 1040, 1131, 1160, 1392, 1508, 1560, 1740, 1885, 2262, 2320, 3016, 3120, 3480, 3770, 4524, 5655, 6032, 6960, 7540, 9048, 11310, 15080, 18096, 22620, 30160, 45240

Step-4: Factors of 90500

List of positive integer factors of 90500 that divides 90480 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 181, 250, 362, 500, 724, 905, 1810, 3620, 4525, 9050, 18100, 22625, 45250

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 90480 and 90500. The biggest common factor number is the GCF number.
So the greatest common factor 90480 and 90500 is 20.

Also check out the Least Common Multiple of 90480 and 90500