What is the Greatest Common Factor of 32144 and 32160?

Greatest common factor (GCF) of 32144 and 32160 is 16.

GCF(32144,32160) = 16

We will now calculate the prime factors of 32144 and 32160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32144 and 32160.

How to find the GCF of 32144 and 32160?

We will first find the prime factorization of 32144 and 32160. After we will calculate the factors of 32144 and 32160 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 32160

Prime factors of 32160 are 2, 3, 5, 67. Prime factorization of 32160 in exponential form is:

32160 = 2⁵ × 3¹ × 5¹ × 67¹

Step-3: Factors of 32144

List of positive integer factors of 32144 that divides 32144 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

Step-4: Factors of 32160

List of positive integer factors of 32160 that divides 32144 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 67, 80, 96, 120, 134, 160, 201, 240, 268, 335, 402, 480, 536, 670, 804, 1005, 1072, 1340, 1608, 2010, 2144, 2680, 3216, 4020, 5360, 6432, 8040, 10720, 16080

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32144 and 32160. The biggest common factor number is the GCF number.
So the greatest common factor 32144 and 32160 is 16.

Also check out the Least Common Multiple of 32144 and 32160