What is the Greatest Common Factor of 1768 and 1785?

Greatest common factor (GCF) of 1768 and 1785 is 17.

GCF(1768,1785) = 17

We will now calculate the prime factors of 1768 and 1785, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1768 and 1785.

How to find the GCF of 1768 and 1785?

We will first find the prime factorization of 1768 and 1785. After we will calculate the factors of 1768 and 1785 and find the biggest common factor number .

Step-1: Prime Factorization of 1768

Prime factors of 1768 are 2, 13, 17. Prime factorization of 1768 in exponential form is:

1768 = 2³ × 13¹ × 17¹

Step-2: Prime Factorization of 1785

Prime factors of 1785 are 3, 5, 7, 17. Prime factorization of 1785 in exponential form is:

1785 = 3¹ × 5¹ × 7¹ × 17¹

Step-3: Factors of 1768

List of positive integer factors of 1768 that divides 1768 without a remainder.

1, 2, 4, 8, 13, 17, 26, 34, 52, 68, 104, 136, 221, 442, 884

Step-4: Factors of 1785

List of positive integer factors of 1785 that divides 1768 without a remainder.

1, 3, 5, 7, 15, 17, 21, 35, 51, 85, 105, 119, 255, 357, 595

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1768 and 1785. The biggest common factor number is the GCF number.
So the greatest common factor 1768 and 1785 is 17.

Also check out the Least Common Multiple of 1768 and 1785