What is the Greatest Common Factor of 25714 and 25722?

Greatest common factor (GCF) of 25714 and 25722 is 2.

GCF(25714,25722) = 2

We will now calculate the prime factors of 25714 and 25722, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25714 and 25722.

How to find the GCF of 25714 and 25722?

We will first find the prime factorization of 25714 and 25722. After we will calculate the factors of 25714 and 25722 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 25722

Prime factors of 25722 are 2, 3, 1429. Prime factorization of 25722 in exponential form is:

25722 = 2¹ × 3² × 1429¹

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 25722

List of positive integer factors of 25722 that divides 25714 without a remainder.

1, 2, 3, 6, 9, 18, 1429, 2858, 4287, 8574, 12861

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25714 and 25722. The biggest common factor number is the GCF number.
So the greatest common factor 25714 and 25722 is 2.

Also check out the Least Common Multiple of 25714 and 25722