What is the Greatest Common Factor of 25714 and 25730?

Greatest common factor (GCF) of 25714 and 25730 is 2.

GCF(25714,25730) = 2

We will now calculate the prime factors of 25714 and 25730, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25714 and 25730.

How to find the GCF of 25714 and 25730?

We will first find the prime factorization of 25714 and 25730. After we will calculate the factors of 25714 and 25730 and find the biggest common factor number .

Step-1: Prime Factorization of 25714

Prime factors of 25714 are 2, 13, 23, 43. Prime factorization of 25714 in exponential form is:

25714 = 2¹ × 13¹ × 23¹ × 43¹

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 25714

List of positive integer factors of 25714 that divides 25714 without a remainder.

1, 2, 13, 23, 26, 43, 46, 86, 299, 559, 598, 989, 1118, 1978, 12857

Step-4: Factors of 25730

List of positive integer factors of 25730 that divides 25714 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 25714 and 25730. The biggest common factor number is the GCF number.
So the greatest common factor 25714 and 25730 is 2.

Also check out the Least Common Multiple of 25714 and 25730