What is the Greatest Common Factor of 67830 and 67845?

Greatest common factor (GCF) of 67830 and 67845 is 15.

GCF(67830,67845) = 15

We will now calculate the prime factors of 67830 and 67845, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67830 and 67845.

How to find the GCF of 67830 and 67845?

We will first find the prime factorization of 67830 and 67845. After we will calculate the factors of 67830 and 67845 and find the biggest common factor number .

Step-1: Prime Factorization of 67830

Prime factors of 67830 are 2, 3, 5, 7, 17, 19. Prime factorization of 67830 in exponential form is:

67830 = 2¹ × 3¹ × 5¹ × 7¹ × 17¹ × 19¹

Step-2: Prime Factorization of 67845

Prime factors of 67845 are 3, 5, 4523. Prime factorization of 67845 in exponential form is:

67845 = 3¹ × 5¹ × 4523¹

Step-3: Factors of 67830

List of positive integer factors of 67830 that divides 67830 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 17, 19, 21, 30, 34, 35, 38, 42, 51, 57, 70, 85, 95, 102, 105, 114, 119, 133, 170, 190, 210, 238, 255, 266, 285, 323, 357, 399, 510, 570, 595, 646, 665, 714, 798, 969, 1190, 1330, 1615, 1785, 1938, 1995, 2261, 3230, 3570, 3990, 4522, 4845, 6783, 9690, 11305, 13566, 22610, 33915

Step-4: Factors of 67845

List of positive integer factors of 67845 that divides 67830 without a remainder.

1, 3, 5, 15, 4523, 13569, 22615

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67830 and 67845. The biggest common factor number is the GCF number.
So the greatest common factor 67830 and 67845 is 15.

Also check out the Least Common Multiple of 67830 and 67845