What is the Greatest Common Factor of 25730 and 25750?

Greatest common factor (GCF) of 25730 and 25750 is 10.

GCF(25730,25750) = 10

We will now calculate the prime factors of 25730 and 25750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25730 and 25750.

How to find the GCF of 25730 and 25750?

We will first find the prime factorization of 25730 and 25750. After we will calculate the factors of 25730 and 25750 and find the biggest common factor number .

Step-1: Prime Factorization of 25730

Prime factors of 25730 are 2, 5, 31, 83. Prime factorization of 25730 in exponential form is:

25730 = 2¹ × 5¹ × 31¹ × 83¹

Step-2: Prime Factorization of 25750

Prime factors of 25750 are 2, 5, 103. Prime factorization of 25750 in exponential form is:

25750 = 2¹ × 5³ × 103¹

Step-3: Factors of 25730

List of positive integer factors of 25730 that divides 25730 without a remainder.

1, 2, 5, 10, 31, 62, 83, 155, 166, 310, 415, 830, 2573, 5146, 12865

Step-4: Factors of 25750

List of positive integer factors of 25750 that divides 25730 without a remainder.

1, 2, 5, 10, 25, 50, 103, 125, 206, 250, 515, 1030, 2575, 5150, 12875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25730 and 25750. The biggest common factor number is the GCF number.
So the greatest common factor 25730 and 25750 is 10.

Also check out the Least Common Multiple of 25730 and 25750