What is the Greatest Common Factor of 75670 and 75684?

Greatest common factor (GCF) of 75670 and 75684 is 14.

GCF(75670,75684) = 14

We will now calculate the prime factors of 75670 and 75684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75670 and 75684.

How to find the GCF of 75670 and 75684?

We will first find the prime factorization of 75670 and 75684. After we will calculate the factors of 75670 and 75684 and find the biggest common factor number .

Step-1: Prime Factorization of 75670

Prime factors of 75670 are 2, 5, 7, 23, 47. Prime factorization of 75670 in exponential form is:

75670 = 2¹ × 5¹ × 7¹ × 23¹ × 47¹

Step-2: Prime Factorization of 75684

Prime factors of 75684 are 2, 3, 7, 17, 53. Prime factorization of 75684 in exponential form is:

75684 = 2² × 3¹ × 7¹ × 17¹ × 53¹

Step-3: Factors of 75670

List of positive integer factors of 75670 that divides 75670 without a remainder.

1, 2, 5, 7, 10, 14, 23, 35, 46, 47, 70, 94, 115, 161, 230, 235, 322, 329, 470, 658, 805, 1081, 1610, 1645, 2162, 3290, 5405, 7567, 10810, 15134, 37835

Step-4: Factors of 75684

List of positive integer factors of 75684 that divides 75670 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 53, 68, 84, 102, 106, 119, 159, 204, 212, 238, 318, 357, 371, 476, 636, 714, 742, 901, 1113, 1428, 1484, 1802, 2226, 2703, 3604, 4452, 5406, 6307, 10812, 12614, 18921, 25228, 37842

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75670 and 75684. The biggest common factor number is the GCF number.
So the greatest common factor 75670 and 75684 is 14.

Also check out the Least Common Multiple of 75670 and 75684