What is the Greatest Common Factor of 1775 and 1785?

Greatest common factor (GCF) of 1775 and 1785 is 5.

GCF(1775,1785) = 5

We will now calculate the prime factors of 1775 and 1785, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1775 and 1785.

How to find the GCF of 1775 and 1785?

We will first find the prime factorization of 1775 and 1785. After we will calculate the factors of 1775 and 1785 and find the biggest common factor number .

Step-1: Prime Factorization of 1775

Prime factors of 1775 are 5, 71. Prime factorization of 1775 in exponential form is:

1775 = 5² × 71¹

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 1775

List of positive integer factors of 1775 that divides 1775 without a remainder.

1, 5, 25, 71, 355

Step-4: Factors of 1785

List of positive integer factors of 1785 that divides 1775 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 1775 and 1785. The biggest common factor number is the GCF number.
So the greatest common factor 1775 and 1785 is 5.

Also check out the Least Common Multiple of 1775 and 1785