What is the Greatest Common Factor of 25724 and 25730?

Greatest common factor (GCF) of 25724 and 25730 is 2.

GCF(25724,25730) = 2

We will now calculate the prime factors of 25724 and 25730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25724 and 25730.

How to find the GCF of 25724 and 25730?

We will first find the prime factorization of 25724 and 25730. After we will calculate the factors of 25724 and 25730 and find the biggest common factor number .

Step-1: Prime Factorization of 25724

Prime factors of 25724 are 2, 59, 109. Prime factorization of 25724 in exponential form is:

25724 = 2² × 59¹ × 109¹

Step-2: 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-3: Factors of 25724

List of positive integer factors of 25724 that divides 25724 without a remainder.

1, 2, 4, 59, 109, 118, 218, 236, 436, 6431, 12862

Step-4: Factors of 25730

List of positive integer factors of 25730 that divides 25724 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25724 and 25730. The biggest common factor number is the GCF number.
So the greatest common factor 25724 and 25730 is 2.

Also check out the Least Common Multiple of 25724 and 25730