What is the Greatest Common Factor of 30996 and 31010?

Greatest common factor (GCF) of 30996 and 31010 is 14.

GCF(30996,31010) = 14

We will now calculate the prime factors of 30996 and 31010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 30996 and 31010.

How to find the GCF of 30996 and 31010?

We will first find the prime factorization of 30996 and 31010. After we will calculate the factors of 30996 and 31010 and find the biggest common factor number .

Step-1: Prime Factorization of 30996

Prime factors of 30996 are 2, 3, 7, 41. Prime factorization of 30996 in exponential form is:

30996 = 2² × 3³ × 7¹ × 41¹

Step-2: Prime Factorization of 31010

Prime factors of 31010 are 2, 5, 7, 443. Prime factorization of 31010 in exponential form is:

31010 = 2¹ × 5¹ × 7¹ × 443¹

Step-3: Factors of 30996

List of positive integer factors of 30996 that divides 30996 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 36, 41, 42, 54, 63, 82, 84, 108, 123, 126, 164, 189, 246, 252, 287, 369, 378, 492, 574, 738, 756, 861, 1107, 1148, 1476, 1722, 2214, 2583, 3444, 4428, 5166, 7749, 10332, 15498

Step-4: Factors of 31010

List of positive integer factors of 31010 that divides 30996 without a remainder.

1, 2, 5, 7, 10, 14, 35, 70, 443, 886, 2215, 3101, 4430, 6202, 15505

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 30996 and 31010. The biggest common factor number is the GCF number.
So the greatest common factor 30996 and 31010 is 14.

Also check out the Least Common Multiple of 30996 and 31010