What is the Greatest Common Factor of 25746 and 25758?

Greatest common factor (GCF) of 25746 and 25758 is 6.

GCF(25746,25758) = 6

We will now calculate the prime factors of 25746 and 25758, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 25746 and 25758.

How to find the GCF of 25746 and 25758?

We will first find the prime factorization of 25746 and 25758. After we will calculate the factors of 25746 and 25758 and find the biggest common factor number .

Step-1: Prime Factorization of 25746

Prime factors of 25746 are 2, 3, 7, 613. Prime factorization of 25746 in exponential form is:

25746 = 2¹ × 3¹ × 7¹ × 613¹

Step-2: Prime Factorization of 25758

Prime factors of 25758 are 2, 3, 53. Prime factorization of 25758 in exponential form is:

25758 = 2¹ × 3⁵ × 53¹

Step-3: Factors of 25746

List of positive integer factors of 25746 that divides 25746 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 613, 1226, 1839, 3678, 4291, 8582, 12873

Step-4: Factors of 25758

List of positive integer factors of 25758 that divides 25746 without a remainder.

1, 2, 3, 6, 9, 18, 27, 53, 54, 81, 106, 159, 162, 243, 318, 477, 486, 954, 1431, 2862, 4293, 8586, 12879

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 25746 and 25758. The biggest common factor number is the GCF number.
So the greatest common factor 25746 and 25758 is 6.

Also check out the Least Common Multiple of 25746 and 25758