What is the Greatest Common Factor of 1765 and 1785?

Greatest common factor (GCF) of 1765 and 1785 is 5.

GCF(1765,1785) = 5

We will now calculate the prime factors of 1765 and 1785, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1765 and 1785.

How to find the GCF of 1765 and 1785?

We will first find the prime factorization of 1765 and 1785. After we will calculate the factors of 1765 and 1785 and find the biggest common factor number .

Step-1: Prime Factorization of 1765

Prime factors of 1765 are 5, 353. Prime factorization of 1765 in exponential form is:

1765 = 5¹ × 353¹

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 1765

List of positive integer factors of 1765 that divides 1765 without a remainder.

1, 5, 353

Step-4: Factors of 1785

List of positive integer factors of 1785 that divides 1765 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 1765 and 1785. The biggest common factor number is the GCF number.
So the greatest common factor 1765 and 1785 is 5.

Also check out the Least Common Multiple of 1765 and 1785