What is the Greatest Common Factor of 10605 and 10625?

Greatest common factor (GCF) of 10605 and 10625 is 5.

GCF(10605,10625) = 5

We will now calculate the prime factors of 10605 and 10625, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10605 and 10625.

How to find the GCF of 10605 and 10625?

We will first find the prime factorization of 10605 and 10625. After we will calculate the factors of 10605 and 10625 and find the biggest common factor number .

Step-1: Prime Factorization of 10605

Prime factors of 10605 are 3, 5, 7, 101. Prime factorization of 10605 in exponential form is:

10605 = 3¹ × 5¹ × 7¹ × 101¹

Step-2: Prime Factorization of 10625

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

10625 = 5⁴ × 17¹

Step-3: Factors of 10605

List of positive integer factors of 10605 that divides 10605 without a remainder.

1, 3, 5, 7, 15, 21, 35, 101, 105, 303, 505, 707, 1515, 2121, 3535

Step-4: Factors of 10625

List of positive integer factors of 10625 that divides 10605 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10605 and 10625. The biggest common factor number is the GCF number.
So the greatest common factor 10605 and 10625 is 5.

Also check out the Least Common Multiple of 10605 and 10625