What is the Greatest Common Factor of 31904 and 31914?

Greatest common factor (GCF) of 31904 and 31914 is 2.

GCF(31904,31914) = 2

We will now calculate the prime factors of 31904 and 31914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31904 and 31914.

How to find the GCF of 31904 and 31914?

We will first find the prime factorization of 31904 and 31914. After we will calculate the factors of 31904 and 31914 and find the biggest common factor number .

Step-1: Prime Factorization of 31904

Prime factors of 31904 are 2, 997. Prime factorization of 31904 in exponential form is:

31904 = 2⁵ × 997¹

Step-2: Prime Factorization of 31914

Prime factors of 31914 are 2, 3, 197. Prime factorization of 31914 in exponential form is:

31914 = 2¹ × 3⁴ × 197¹

Step-3: Factors of 31904

List of positive integer factors of 31904 that divides 31904 without a remainder.

1, 2, 4, 8, 16, 32, 997, 1994, 3988, 7976, 15952

Step-4: Factors of 31914

List of positive integer factors of 31914 that divides 31904 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 197, 394, 591, 1182, 1773, 3546, 5319, 10638, 15957

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31904 and 31914. The biggest common factor number is the GCF number.
So the greatest common factor 31904 and 31914 is 2.

Also check out the Least Common Multiple of 31904 and 31914