What is the Greatest Common Factor of 75684 and 75693?

Greatest common factor (GCF) of 75684 and 75693 is 3.

GCF(75684,75693) = 3

We will now calculate the prime factors of 75684 and 75693, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75684 and 75693.

How to find the GCF of 75684 and 75693?

We will first find the prime factorization of 75684 and 75693. After we will calculate the factors of 75684 and 75693 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 75693

Prime factors of 75693 are 3, 23, 1097. Prime factorization of 75693 in exponential form is:

75693 = 3¹ × 23¹ × 1097¹

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 75693

List of positive integer factors of 75693 that divides 75684 without a remainder.

1, 3, 23, 69, 1097, 3291, 25231

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75684 and 75693. The biggest common factor number is the GCF number.
So the greatest common factor 75684 and 75693 is 3.

Also check out the Least Common Multiple of 75684 and 75693