What is the Greatest Common Factor of 10625 and 10634?

Greatest common factor (GCF) of 10625 and 10634 is 1.

GCF(10625,10634) = 1

We will now calculate the prime factors of 10625 and 10634, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10625 and 10634.

How to find the GCF of 10625 and 10634?

We will first find the prime factorization of 10625 and 10634. After we will calculate the factors of 10625 and 10634 and find the biggest common factor number .

Step-1: Prime Factorization of 10625

Prime factors of 10625 are 5, 17. Prime factorization of 10625 in exponential form is:

10625 = 5⁴ × 17¹

Step-2: Prime Factorization of 10634

Prime factors of 10634 are 2, 13, 409. Prime factorization of 10634 in exponential form is:

10634 = 2¹ × 13¹ × 409¹

Step-3: Factors of 10625

List of positive integer factors of 10625 that divides 10625 without a remainder.

1, 5, 17, 25, 85, 125, 425, 625, 2125

Step-4: Factors of 10634

List of positive integer factors of 10634 that divides 10625 without a remainder.

1, 2, 13, 26, 409, 818, 5317

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10625 and 10634. The biggest common factor number is the GCF number.
So the greatest common factor 10625 and 10634 is 1.

Also check out the Least Common Multiple of 10625 and 10634