What is the Greatest Common Factor of 37723 and 37740?

Greatest common factor (GCF) of 37723 and 37740 is 17.

GCF(37723,37740) = 17

We will now calculate the prime factors of 37723 and 37740, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37723 and 37740.

How to find the GCF of 37723 and 37740?

We will first find the prime factorization of 37723 and 37740. After we will calculate the factors of 37723 and 37740 and find the biggest common factor number .

Step-1: Prime Factorization of 37723

Prime factors of 37723 are 7, 17, 317. Prime factorization of 37723 in exponential form is:

37723 = 7¹ × 17¹ × 317¹

Step-2: Prime Factorization of 37740

Prime factors of 37740 are 2, 3, 5, 17, 37. Prime factorization of 37740 in exponential form is:

37740 = 2² × 3¹ × 5¹ × 17¹ × 37¹

Step-3: Factors of 37723

List of positive integer factors of 37723 that divides 37723 without a remainder.

1, 7, 17, 119, 317, 2219, 5389

Step-4: Factors of 37740

List of positive integer factors of 37740 that divides 37723 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 30, 34, 37, 51, 60, 68, 74, 85, 102, 111, 148, 170, 185, 204, 222, 255, 340, 370, 444, 510, 555, 629, 740, 1020, 1110, 1258, 1887, 2220, 2516, 3145, 3774, 6290, 7548, 9435, 12580, 18870

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37723 and 37740. The biggest common factor number is the GCF number.
So the greatest common factor 37723 and 37740 is 17.

Also check out the Least Common Multiple of 37723 and 37740