What is the Greatest Common Factor of 34625 and 34640?

Greatest common factor (GCF) of 34625 and 34640 is 5.

GCF(34625,34640) = 5

We will now calculate the prime factors of 34625 and 34640, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34625 and 34640.

How to find the GCF of 34625 and 34640?

We will first find the prime factorization of 34625 and 34640. After we will calculate the factors of 34625 and 34640 and find the biggest common factor number .

Step-1: Prime Factorization of 34625

Prime factors of 34625 are 5, 277. Prime factorization of 34625 in exponential form is:

34625 = 5³ × 277¹

Step-2: Prime Factorization of 34640

Prime factors of 34640 are 2, 5, 433. Prime factorization of 34640 in exponential form is:

34640 = 2⁴ × 5¹ × 433¹

Step-3: Factors of 34625

List of positive integer factors of 34625 that divides 34625 without a remainder.

1, 5, 25, 125, 277, 1385, 6925

Step-4: Factors of 34640

List of positive integer factors of 34640 that divides 34625 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 433, 866, 1732, 2165, 3464, 4330, 6928, 8660, 17320

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34625 and 34640. The biggest common factor number is the GCF number.
So the greatest common factor 34625 and 34640 is 5.

Also check out the Least Common Multiple of 34625 and 34640