What is the Greatest Common Factor of 37740 and 37746?

Greatest common factor (GCF) of 37740 and 37746 is 6.

GCF(37740,37746) = 6

We will now calculate the prime factors of 37740 and 37746, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37740 and 37746.

How to find the GCF of 37740 and 37746?

We will first find the prime factorization of 37740 and 37746. After we will calculate the factors of 37740 and 37746 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 37746

Prime factors of 37746 are 2, 3, 233. Prime factorization of 37746 in exponential form is:

37746 = 2¹ × 3⁴ × 233¹

Step-3: Factors of 37740

List of positive integer factors of 37740 that divides 37740 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

Step-4: Factors of 37746

List of positive integer factors of 37746 that divides 37740 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 233, 466, 699, 1398, 2097, 4194, 6291, 12582, 18873

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37740 and 37746. The biggest common factor number is the GCF number.
So the greatest common factor 37740 and 37746 is 6.

Also check out the Least Common Multiple of 37740 and 37746