What is the Greatest Common Factor of 31900 and 31914?

Greatest common factor (GCF) of 31900 and 31914 is 2.

GCF(31900,31914) = 2

We will now calculate the prime factors of 31900 and 31914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 31900 and 31914.

How to find the GCF of 31900 and 31914?

We will first find the prime factorization of 31900 and 31914. After we will calculate the factors of 31900 and 31914 and find the biggest common factor number .

Step-1: Prime Factorization of 31900

Prime factors of 31900 are 2, 5, 11, 29. Prime factorization of 31900 in exponential form is:

31900 = 2² × 5² × 11¹ × 29¹

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 31900

List of positive integer factors of 31900 that divides 31900 without a remainder.

1, 2, 4, 5, 10, 11, 20, 22, 25, 29, 44, 50, 55, 58, 100, 110, 116, 145, 220, 275, 290, 319, 550, 580, 638, 725, 1100, 1276, 1450, 1595, 2900, 3190, 6380, 7975, 15950

Step-4: Factors of 31914

List of positive integer factors of 31914 that divides 31900 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 31900 and 31914. The biggest common factor number is the GCF number.
So the greatest common factor 31900 and 31914 is 2.

Also check out the Least Common Multiple of 31900 and 31914