What is the Greatest Common Factor of 32130 and 32144?

Greatest common factor (GCF) of 32130 and 32144 is 14.

GCF(32130,32144) = 14

We will now calculate the prime factors of 32130 and 32144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32130 and 32144.

How to find the GCF of 32130 and 32144?

We will first find the prime factorization of 32130 and 32144. After we will calculate the factors of 32130 and 32144 and find the biggest common factor number .

Step-1: Prime Factorization of 32130

Prime factors of 32130 are 2, 3, 5, 7, 17. Prime factorization of 32130 in exponential form is:

32130 = 2¹ × 3³ × 5¹ × 7¹ × 17¹

Step-2: Prime Factorization of 32144

Prime factors of 32144 are 2, 7, 41. Prime factorization of 32144 in exponential form is:

32144 = 2⁴ × 7² × 41¹

Step-3: Factors of 32130

List of positive integer factors of 32130 that divides 32130 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 17, 18, 21, 27, 30, 34, 35, 42, 45, 51, 54, 63, 70, 85, 90, 102, 105, 119, 126, 135, 153, 170, 189, 210, 238, 255, 270, 306, 315, 357, 378, 459, 510, 595, 630, 714, 765, 918, 945, 1071, 1190, 1530, 1785, 1890, 2142, 2295, 3213, 3570, 4590, 5355, 6426, 10710, 16065

Step-4: Factors of 32144

List of positive integer factors of 32144 that divides 32130 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 41, 49, 56, 82, 98, 112, 164, 196, 287, 328, 392, 574, 656, 784, 1148, 2009, 2296, 4018, 4592, 8036, 16072

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32130 and 32144. The biggest common factor number is the GCF number.
So the greatest common factor 32130 and 32144 is 14.

Also check out the Least Common Multiple of 32130 and 32144