What is the Greatest Common Factor of 27300 and 27319?

Greatest common factor (GCF) of 27300 and 27319 is 1.

GCF(27300,27319) = 1

We will now calculate the prime factors of 27300 and 27319, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 27300 and 27319.

How to find the GCF of 27300 and 27319?

We will first find the prime factorization of 27300 and 27319. After we will calculate the factors of 27300 and 27319 and find the biggest common factor number .

Step-1: Prime Factorization of 27300

Prime factors of 27300 are 2, 3, 5, 7, 13. Prime factorization of 27300 in exponential form is:

27300 = 2² × 3¹ × 5² × 7¹ × 13¹

Step-2: Prime Factorization of 27319

Prime factors of 27319 are 17, 1607. Prime factorization of 27319 in exponential form is:

27319 = 17¹ × 1607¹

Step-3: Factors of 27300

List of positive integer factors of 27300 that divides 27300 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 25, 26, 28, 30, 35, 39, 42, 50, 52, 60, 65, 70, 75, 78, 84, 91, 100, 105, 130, 140, 150, 156, 175, 182, 195, 210, 260, 273, 300, 325, 350, 364, 390, 420, 455, 525, 546, 650, 700, 780, 910, 975, 1050, 1092, 1300, 1365, 1820, 1950, 2100, 2275, 2730, 3900, 4550, 5460, 6825, 9100, 13650

Step-4: Factors of 27319

List of positive integer factors of 27319 that divides 27300 without a remainder.

1, 17, 1607

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 27300 and 27319. The biggest common factor number is the GCF number.
So the greatest common factor 27300 and 27319 is 1.

Also check out the Least Common Multiple of 27300 and 27319