What is the Greatest Common Factor of 34765 and 34782?

Greatest common factor (GCF) of 34765 and 34782 is 17.

GCF(34765,34782) = 17

We will now calculate the prime factors of 34765 and 34782, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34765 and 34782.

How to find the GCF of 34765 and 34782?

We will first find the prime factorization of 34765 and 34782. After we will calculate the factors of 34765 and 34782 and find the biggest common factor number .

Step-1: Prime Factorization of 34765

Prime factors of 34765 are 5, 17, 409. Prime factorization of 34765 in exponential form is:

34765 = 5¹ × 17¹ × 409¹

Step-2: Prime Factorization of 34782

Prime factors of 34782 are 2, 3, 11, 17, 31. Prime factorization of 34782 in exponential form is:

34782 = 2¹ × 3¹ × 11¹ × 17¹ × 31¹

Step-3: Factors of 34765

List of positive integer factors of 34765 that divides 34765 without a remainder.

1, 5, 17, 85, 409, 2045, 6953

Step-4: Factors of 34782

List of positive integer factors of 34782 that divides 34765 without a remainder.

1, 2, 3, 6, 11, 17, 22, 31, 33, 34, 51, 62, 66, 93, 102, 186, 187, 341, 374, 527, 561, 682, 1023, 1054, 1122, 1581, 2046, 3162, 5797, 11594, 17391

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34765 and 34782. The biggest common factor number is the GCF number.
So the greatest common factor 34765 and 34782 is 17.

Also check out the Least Common Multiple of 34765 and 34782