What is the Greatest Common Factor of 35606 and 35625?

Greatest common factor (GCF) of 35606 and 35625 is 19.

GCF(35606,35625) = 19

We will now calculate the prime factors of 35606 and 35625, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35606 and 35625.

How to find the GCF of 35606 and 35625?

We will first find the prime factorization of 35606 and 35625. After we will calculate the factors of 35606 and 35625 and find the biggest common factor number .

Step-1: Prime Factorization of 35606

Prime factors of 35606 are 2, 19, 937. Prime factorization of 35606 in exponential form is:

35606 = 2¹ × 19¹ × 937¹

Step-2: Prime Factorization of 35625

Prime factors of 35625 are 3, 5, 19. Prime factorization of 35625 in exponential form is:

35625 = 3¹ × 5⁴ × 19¹

Step-3: Factors of 35606

List of positive integer factors of 35606 that divides 35606 without a remainder.

1, 2, 19, 38, 937, 1874, 17803

Step-4: Factors of 35625

List of positive integer factors of 35625 that divides 35606 without a remainder.

1, 3, 5, 15, 19, 25, 57, 75, 95, 125, 285, 375, 475, 625, 1425, 1875, 2375, 7125, 11875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35606 and 35625. The biggest common factor number is the GCF number.
So the greatest common factor 35606 and 35625 is 19.

Also check out the Least Common Multiple of 35606 and 35625