What is the Greatest Common Factor of 37605 and 37620?

Greatest common factor (GCF) of 37605 and 37620 is 15.

GCF(37605,37620) = 15

We will now calculate the prime factors of 37605 and 37620, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37605 and 37620.

How to find the GCF of 37605 and 37620?

We will first find the prime factorization of 37605 and 37620. After we will calculate the factors of 37605 and 37620 and find the biggest common factor number .

Step-1: Prime Factorization of 37605

Prime factors of 37605 are 3, 5, 23, 109. Prime factorization of 37605 in exponential form is:

37605 = 3¹ × 5¹ × 23¹ × 109¹

Step-2: Prime Factorization of 37620

Prime factors of 37620 are 2, 3, 5, 11, 19. Prime factorization of 37620 in exponential form is:

37620 = 2² × 3² × 5¹ × 11¹ × 19¹

Step-3: Factors of 37605

List of positive integer factors of 37605 that divides 37605 without a remainder.

1, 3, 5, 15, 23, 69, 109, 115, 327, 345, 545, 1635, 2507, 7521, 12535

Step-4: Factors of 37620

List of positive integer factors of 37620 that divides 37605 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 19, 20, 22, 30, 33, 36, 38, 44, 45, 55, 57, 60, 66, 76, 90, 95, 99, 110, 114, 132, 165, 171, 180, 190, 198, 209, 220, 228, 285, 330, 342, 380, 396, 418, 495, 570, 627, 660, 684, 836, 855, 990, 1045, 1140, 1254, 1710, 1881, 1980, 2090, 2508, 3135, 3420, 3762, 4180, 6270, 7524, 9405, 12540, 18810

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37605 and 37620. The biggest common factor number is the GCF number.
So the greatest common factor 37605 and 37620 is 15.

Also check out the Least Common Multiple of 37605 and 37620