What is the Greatest Common Factor of 75684 and 75698?

Greatest common factor (GCF) of 75684 and 75698 is 14.

GCF(75684,75698) = 14

We will now calculate the prime factors of 75684 and 75698, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75684 and 75698.

How to find the GCF of 75684 and 75698?

We will first find the prime factorization of 75684 and 75698. After we will calculate the factors of 75684 and 75698 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75698

Prime factors of 75698 are 2, 7, 5407. Prime factorization of 75698 in exponential form is:

75698 = 2¹ × 7¹ × 5407¹

Step-3: Factors of 75684

List of positive integer factors of 75684 that divides 75684 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

Step-4: Factors of 75698

List of positive integer factors of 75698 that divides 75684 without a remainder.

1, 2, 7, 14, 5407, 10814, 37849

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75684 and 75698. The biggest common factor number is the GCF number.
So the greatest common factor 75684 and 75698 is 14.

Also check out the Least Common Multiple of 75684 and 75698