What is the Greatest Common Factor of 31914 and 31932?

Greatest common factor (GCF) of 31914 and 31932 is 18.

GCF(31914,31932) = 18

We will now calculate the prime factors of 31914 and 31932, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31914 and 31932.

How to find the GCF of 31914 and 31932?

We will first find the prime factorization of 31914 and 31932. After we will calculate the factors of 31914 and 31932 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 31932

Prime factors of 31932 are 2, 3, 887. Prime factorization of 31932 in exponential form is:

31932 = 2² × 3² × 887¹

Step-3: Factors of 31914

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

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

Step-4: Factors of 31932

List of positive integer factors of 31932 that divides 31914 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 887, 1774, 2661, 3548, 5322, 7983, 10644, 15966

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 31914 and 31932. The biggest common factor number is the GCF number.
So the greatest common factor 31914 and 31932 is 18.

Also check out the Least Common Multiple of 31914 and 31932