What is the Greatest Common Factor of 75690 and 75705?

Greatest common factor (GCF) of 75690 and 75705 is 15.

GCF(75690,75705) = 15

We will now calculate the prime factors of 75690 and 75705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75690 and 75705.

How to find the GCF of 75690 and 75705?

We will first find the prime factorization of 75690 and 75705. After we will calculate the factors of 75690 and 75705 and find the biggest common factor number .

Step-1: Prime Factorization of 75690

Prime factors of 75690 are 2, 3, 5, 29. Prime factorization of 75690 in exponential form is:

75690 = 2¹ × 3² × 5¹ × 29²

Step-2: Prime Factorization of 75705

Prime factors of 75705 are 3, 5, 7, 103. Prime factorization of 75705 in exponential form is:

75705 = 3¹ × 5¹ × 7² × 103¹

Step-3: Factors of 75690

List of positive integer factors of 75690 that divides 75690 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 29, 30, 45, 58, 87, 90, 145, 174, 261, 290, 435, 522, 841, 870, 1305, 1682, 2523, 2610, 4205, 5046, 7569, 8410, 12615, 15138, 25230, 37845

Step-4: Factors of 75705

List of positive integer factors of 75705 that divides 75690 without a remainder.

1, 3, 5, 7, 15, 21, 35, 49, 103, 105, 147, 245, 309, 515, 721, 735, 1545, 2163, 3605, 5047, 10815, 15141, 25235

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75690 and 75705. The biggest common factor number is the GCF number.
So the greatest common factor 75690 and 75705 is 15.

Also check out the Least Common Multiple of 75690 and 75705