What is the Greatest Common Factor of 31755 and 31770?

Greatest common factor (GCF) of 31755 and 31770 is 15.

GCF(31755,31770) = 15

We will now calculate the prime factors of 31755 and 31770, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31755 and 31770.

How to find the GCF of 31755 and 31770?

We will first find the prime factorization of 31755 and 31770. After we will calculate the factors of 31755 and 31770 and find the biggest common factor number .

Step-1: Prime Factorization of 31755

Prime factors of 31755 are 3, 5, 29, 73. Prime factorization of 31755 in exponential form is:

31755 = 3¹ × 5¹ × 29¹ × 73¹

Step-2: 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-3: Factors of 31755

List of positive integer factors of 31755 that divides 31755 without a remainder.

1, 3, 5, 15, 29, 73, 87, 145, 219, 365, 435, 1095, 2117, 6351, 10585

Step-4: Factors of 31770

List of positive integer factors of 31770 that divides 31755 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31755 and 31770. The biggest common factor number is the GCF number.
So the greatest common factor 31755 and 31770 is 15.

Also check out the Least Common Multiple of 31755 and 31770