What is the Greatest Common Factor of 90300 and 90314?

Greatest common factor (GCF) of 90300 and 90314 is 14.

GCF(90300,90314) = 14

We will now calculate the prime factors of 90300 and 90314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 90300 and 90314.

How to find the GCF of 90300 and 90314?

We will first find the prime factorization of 90300 and 90314. After we will calculate the factors of 90300 and 90314 and find the biggest common factor number .

Step-1: Prime Factorization of 90300

Prime factors of 90300 are 2, 3, 5, 7, 43. Prime factorization of 90300 in exponential form is:

90300 = 2² × 3¹ × 5² × 7¹ × 43¹

Step-2: Prime Factorization of 90314

Prime factors of 90314 are 2, 7, 6451. Prime factorization of 90314 in exponential form is:

90314 = 2¹ × 7¹ × 6451¹

Step-3: Factors of 90300

List of positive integer factors of 90300 that divides 90300 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 43, 50, 60, 70, 75, 84, 86, 100, 105, 129, 140, 150, 172, 175, 210, 215, 258, 300, 301, 350, 420, 430, 516, 525, 602, 645, 700, 860, 903, 1050, 1075, 1204, 1290, 1505, 1806, 2100, 2150, 2580, 3010, 3225, 3612, 4300, 4515, 6020, 6450, 7525, 9030, 12900, 15050, 18060, 22575, 30100, 45150

Step-4: Factors of 90314

List of positive integer factors of 90314 that divides 90300 without a remainder.

1, 2, 7, 14, 6451, 12902, 45157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 90300 and 90314. The biggest common factor number is the GCF number.
So the greatest common factor 90300 and 90314 is 14.

Also check out the Least Common Multiple of 90300 and 90314