What is the Greatest Common Factor of 32900 and 32914?

Greatest common factor (GCF) of 32900 and 32914 is 14.

GCF(32900,32914) = 14

We will now calculate the prime factors of 32900 and 32914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32900 and 32914.

How to find the GCF of 32900 and 32914?

We will first find the prime factorization of 32900 and 32914. After we will calculate the factors of 32900 and 32914 and find the biggest common factor number .

Step-1: Prime Factorization of 32900

Prime factors of 32900 are 2, 5, 7, 47. Prime factorization of 32900 in exponential form is:

32900 = 2² × 5² × 7¹ × 47¹

Step-2: Prime Factorization of 32914

Prime factors of 32914 are 2, 7, 2351. Prime factorization of 32914 in exponential form is:

32914 = 2¹ × 7¹ × 2351¹

Step-3: Factors of 32900

List of positive integer factors of 32900 that divides 32900 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 47, 50, 70, 94, 100, 140, 175, 188, 235, 329, 350, 470, 658, 700, 940, 1175, 1316, 1645, 2350, 3290, 4700, 6580, 8225, 16450

Step-4: Factors of 32914

List of positive integer factors of 32914 that divides 32900 without a remainder.

1, 2, 7, 14, 2351, 4702, 16457

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32900 and 32914. The biggest common factor number is the GCF number.
So the greatest common factor 32900 and 32914 is 14.

Also check out the Least Common Multiple of 32900 and 32914