What is the Greatest Common Factor of 67814 and 67830?

Greatest common factor (GCF) of 67814 and 67830 is 2.

GCF(67814,67830) = 2

We will now calculate the prime factors of 67814 and 67830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67814 and 67830.

How to find the GCF of 67814 and 67830?

We will first find the prime factorization of 67814 and 67830. After we will calculate the factors of 67814 and 67830 and find the biggest common factor number .

Step-1: Prime Factorization of 67814

Prime factors of 67814 are 2, 41, 827. Prime factorization of 67814 in exponential form is:

67814 = 2¹ × 41¹ × 827¹

Step-2: 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-3: Factors of 67814

List of positive integer factors of 67814 that divides 67814 without a remainder.

1, 2, 41, 82, 827, 1654, 33907

Step-4: Factors of 67830

List of positive integer factors of 67830 that divides 67814 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67814 and 67830. The biggest common factor number is the GCF number.
So the greatest common factor 67814 and 67830 is 2.

Also check out the Least Common Multiple of 67814 and 67830