What is the Greatest Common Factor of 32114 and 32130?

Greatest common factor (GCF) of 32114 and 32130 is 2.

GCF(32114,32130) = 2

We will now calculate the prime factors of 32114 and 32130, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32114 and 32130.

How to find the GCF of 32114 and 32130?

We will first find the prime factorization of 32114 and 32130. After we will calculate the factors of 32114 and 32130 and find the biggest common factor number .

Step-1: Prime Factorization of 32114

Prime factors of 32114 are 2, 16057. Prime factorization of 32114 in exponential form is:

32114 = 2¹ × 16057¹

Step-2: 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-3: Factors of 32114

List of positive integer factors of 32114 that divides 32114 without a remainder.

1, 2, 16057

Step-4: Factors of 32130

List of positive integer factors of 32130 that divides 32114 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32114 and 32130. The biggest common factor number is the GCF number.
So the greatest common factor 32114 and 32130 is 2.

Also check out the Least Common Multiple of 32114 and 32130