What is the Greatest Common Factor of 32130 and 32140?

Greatest common factor (GCF) of 32130 and 32140 is 10.

GCF(32130,32140) = 10

We will now calculate the prime factors of 32130 and 32140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32130 and 32140.

How to find the GCF of 32130 and 32140?

We will first find the prime factorization of 32130 and 32140. After we will calculate the factors of 32130 and 32140 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 32140

Prime factors of 32140 are 2, 5, 1607. Prime factorization of 32140 in exponential form is:

32140 = 2² × 5¹ × 1607¹

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 32140

List of positive integer factors of 32140 that divides 32130 without a remainder.

1, 2, 4, 5, 10, 20, 1607, 3214, 6428, 8035, 16070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32130 and 32140. The biggest common factor number is the GCF number.
So the greatest common factor 32130 and 32140 is 10.

Also check out the Least Common Multiple of 32130 and 32140