What is the Greatest Common Factor of 31996 and 32010?

Greatest common factor (GCF) of 31996 and 32010 is 2.

GCF(31996,32010) = 2

We will now calculate the prime factors of 31996 and 32010, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31996 and 32010.

How to find the GCF of 31996 and 32010?

We will first find the prime factorization of 31996 and 32010. After we will calculate the factors of 31996 and 32010 and find the biggest common factor number .

Step-1: Prime Factorization of 31996

Prime factors of 31996 are 2, 19, 421. Prime factorization of 31996 in exponential form is:

31996 = 2² × 19¹ × 421¹

Step-2: Prime Factorization of 32010

Prime factors of 32010 are 2, 3, 5, 11, 97. Prime factorization of 32010 in exponential form is:

32010 = 2¹ × 3¹ × 5¹ × 11¹ × 97¹

Step-3: Factors of 31996

List of positive integer factors of 31996 that divides 31996 without a remainder.

1, 2, 4, 19, 38, 76, 421, 842, 1684, 7999, 15998

Step-4: Factors of 32010

List of positive integer factors of 32010 that divides 31996 without a remainder.

1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 97, 110, 165, 194, 291, 330, 485, 582, 970, 1067, 1455, 2134, 2910, 3201, 5335, 6402, 10670, 16005

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31996 and 32010. The biggest common factor number is the GCF number.
So the greatest common factor 31996 and 32010 is 2.

Also check out the Least Common Multiple of 31996 and 32010