What is the Greatest Common Factor of 25900 and 25914?

Greatest common factor (GCF) of 25900 and 25914 is 14.

GCF(25900,25914) = 14

We will now calculate the prime factors of 25900 and 25914, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25900 and 25914.

How to find the GCF of 25900 and 25914?

We will first find the prime factorization of 25900 and 25914. After we will calculate the factors of 25900 and 25914 and find the biggest common factor number .

Step-1: Prime Factorization of 25900

Prime factors of 25900 are 2, 5, 7, 37. Prime factorization of 25900 in exponential form is:

25900 = 2² × 5² × 7¹ × 37¹

Step-2: Prime Factorization of 25914

Prime factors of 25914 are 2, 3, 7, 617. Prime factorization of 25914 in exponential form is:

25914 = 2¹ × 3¹ × 7¹ × 617¹

Step-3: Factors of 25900

List of positive integer factors of 25900 that divides 25900 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 37, 50, 70, 74, 100, 140, 148, 175, 185, 259, 350, 370, 518, 700, 740, 925, 1036, 1295, 1850, 2590, 3700, 5180, 6475, 12950

Step-4: Factors of 25914

List of positive integer factors of 25914 that divides 25900 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 617, 1234, 1851, 3702, 4319, 8638, 12957

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25900 and 25914. The biggest common factor number is the GCF number.
So the greatest common factor 25900 and 25914 is 14.

Also check out the Least Common Multiple of 25900 and 25914