What is the Greatest Common Factor of 37170 and 37184?

Greatest common factor (GCF) of 37170 and 37184 is 14.

GCF(37170,37184) = 14

We will now calculate the prime factors of 37170 and 37184, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 37170 and 37184.

How to find the GCF of 37170 and 37184?

We will first find the prime factorization of 37170 and 37184. After we will calculate the factors of 37170 and 37184 and find the biggest common factor number .

Step-1: Prime Factorization of 37170

Prime factors of 37170 are 2, 3, 5, 7, 59. Prime factorization of 37170 in exponential form is:

37170 = 2¹ × 3² × 5¹ × 7¹ × 59¹

Step-2: Prime Factorization of 37184

Prime factors of 37184 are 2, 7, 83. Prime factorization of 37184 in exponential form is:

37184 = 2⁶ × 7¹ × 83¹

Step-3: Factors of 37170

List of positive integer factors of 37170 that divides 37170 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 59, 63, 70, 90, 105, 118, 126, 177, 210, 295, 315, 354, 413, 531, 590, 630, 826, 885, 1062, 1239, 1770, 2065, 2478, 2655, 3717, 4130, 5310, 6195, 7434, 12390, 18585

Step-4: Factors of 37184

List of positive integer factors of 37184 that divides 37170 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 83, 112, 166, 224, 332, 448, 581, 664, 1162, 1328, 2324, 2656, 4648, 5312, 9296, 18592

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 37170 and 37184. The biggest common factor number is the GCF number.
So the greatest common factor 37170 and 37184 is 14.

Also check out the Least Common Multiple of 37170 and 37184