What is the Greatest Common Factor of 16745 and 16762?

Greatest common factor (GCF) of 16745 and 16762 is 17.

GCF(16745,16762) = 17

We will now calculate the prime factors of 16745 and 16762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16745 and 16762.

How to find the GCF of 16745 and 16762?

We will first find the prime factorization of 16745 and 16762. After we will calculate the factors of 16745 and 16762 and find the biggest common factor number .

Step-1: Prime Factorization of 16745

Prime factors of 16745 are 5, 17, 197. Prime factorization of 16745 in exponential form is:

16745 = 5¹ × 17¹ × 197¹

Step-2: Prime Factorization of 16762

Prime factors of 16762 are 2, 17, 29. Prime factorization of 16762 in exponential form is:

16762 = 2¹ × 17² × 29¹

Step-3: Factors of 16745

List of positive integer factors of 16745 that divides 16745 without a remainder.

1, 5, 17, 85, 197, 985, 3349

Step-4: Factors of 16762

List of positive integer factors of 16762 that divides 16745 without a remainder.

1, 2, 17, 29, 34, 58, 289, 493, 578, 986, 8381

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16745 and 16762. The biggest common factor number is the GCF number.
So the greatest common factor 16745 and 16762 is 17.

Also check out the Least Common Multiple of 16745 and 16762