What is the Greatest Common Factor of 31740 and 31749?

Greatest common factor (GCF) of 31740 and 31749 is 3.

GCF(31740,31749) = 3

We will now calculate the prime factors of 31740 and 31749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31740 and 31749.

How to find the GCF of 31740 and 31749?

We will first find the prime factorization of 31740 and 31749. After we will calculate the factors of 31740 and 31749 and find the biggest common factor number .

Step-1: Prime Factorization of 31740

Prime factors of 31740 are 2, 3, 5, 23. Prime factorization of 31740 in exponential form is:

31740 = 2² × 3¹ × 5¹ × 23²

Step-2: Prime Factorization of 31749

Prime factors of 31749 are 3, 19, 557. Prime factorization of 31749 in exponential form is:

31749 = 3¹ × 19¹ × 557¹

Step-3: Factors of 31740

List of positive integer factors of 31740 that divides 31740 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 69, 92, 115, 138, 230, 276, 345, 460, 529, 690, 1058, 1380, 1587, 2116, 2645, 3174, 5290, 6348, 7935, 10580, 15870

Step-4: Factors of 31749

List of positive integer factors of 31749 that divides 31740 without a remainder.

1, 3, 19, 57, 557, 1671, 10583

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31740 and 31749. The biggest common factor number is the GCF number.
So the greatest common factor 31740 and 31749 is 3.

Also check out the Least Common Multiple of 31740 and 31749