What is the Greatest Common Factor of 31770 and 31775?

Greatest common factor (GCF) of 31770 and 31775 is 5.

GCF(31770,31775) = 5

We will now calculate the prime factors of 31770 and 31775, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31770 and 31775.

How to find the GCF of 31770 and 31775?

We will first find the prime factorization of 31770 and 31775. After we will calculate the factors of 31770 and 31775 and find the biggest common factor number .

Step-1: Prime Factorization of 31770

Prime factors of 31770 are 2, 3, 5, 353. Prime factorization of 31770 in exponential form is:

31770 = 2¹ × 3² × 5¹ × 353¹

Step-2: Prime Factorization of 31775

Prime factors of 31775 are 5, 31, 41. Prime factorization of 31775 in exponential form is:

31775 = 5² × 31¹ × 41¹

Step-3: Factors of 31770

List of positive integer factors of 31770 that divides 31770 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 353, 706, 1059, 1765, 2118, 3177, 3530, 5295, 6354, 10590, 15885

Step-4: Factors of 31775

List of positive integer factors of 31775 that divides 31770 without a remainder.

1, 5, 25, 31, 41, 155, 205, 775, 1025, 1271, 6355

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31770 and 31775. The biggest common factor number is the GCF number.
So the greatest common factor 31770 and 31775 is 5.

Also check out the Least Common Multiple of 31770 and 31775