What is the Greatest Common Factor of 68310 and 68320?

Greatest common factor (GCF) of 68310 and 68320 is 10.

GCF(68310,68320) = 10

We will now calculate the prime factors of 68310 and 68320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 68310 and 68320.

How to find the GCF of 68310 and 68320?

We will first find the prime factorization of 68310 and 68320. After we will calculate the factors of 68310 and 68320 and find the biggest common factor number .

Step-1: Prime Factorization of 68310

Prime factors of 68310 are 2, 3, 5, 11, 23. Prime factorization of 68310 in exponential form is:

68310 = 2¹ × 3³ × 5¹ × 11¹ × 23¹

Step-2: Prime Factorization of 68320

Prime factors of 68320 are 2, 5, 7, 61. Prime factorization of 68320 in exponential form is:

68320 = 2⁵ × 5¹ × 7¹ × 61¹

Step-3: Factors of 68310

List of positive integer factors of 68310 that divides 68310 without a remainder.

1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 23, 27, 30, 33, 45, 46, 54, 55, 66, 69, 90, 99, 110, 115, 135, 138, 165, 198, 207, 230, 253, 270, 297, 330, 345, 414, 495, 506, 594, 621, 690, 759, 990, 1035, 1242, 1265, 1485, 1518, 2070, 2277, 2530, 2970, 3105, 3795, 4554, 6210, 6831, 7590, 11385, 13662, 22770, 34155

Step-4: Factors of 68320

List of positive integer factors of 68320 that divides 68310 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 56, 61, 70, 80, 112, 122, 140, 160, 224, 244, 280, 305, 427, 488, 560, 610, 854, 976, 1120, 1220, 1708, 1952, 2135, 2440, 3416, 4270, 4880, 6832, 8540, 9760, 13664, 17080, 34160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 68310 and 68320. The biggest common factor number is the GCF number.
So the greatest common factor 68310 and 68320 is 10.

Also check out the Least Common Multiple of 68310 and 68320