What is the Greatest Common Factor of 34880 and 34900?

Greatest common factor (GCF) of 34880 and 34900 is 20.

GCF(34880,34900) = 20

We will now calculate the prime factors of 34880 and 34900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34880 and 34900.

How to find the GCF of 34880 and 34900?

We will first find the prime factorization of 34880 and 34900. After we will calculate the factors of 34880 and 34900 and find the biggest common factor number .

Step-1: Prime Factorization of 34880

Prime factors of 34880 are 2, 5, 109. Prime factorization of 34880 in exponential form is:

34880 = 2⁶ × 5¹ × 109¹

Step-2: Prime Factorization of 34900

Prime factors of 34900 are 2, 5, 349. Prime factorization of 34900 in exponential form is:

34900 = 2² × 5² × 349¹

Step-3: Factors of 34880

List of positive integer factors of 34880 that divides 34880 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 109, 160, 218, 320, 436, 545, 872, 1090, 1744, 2180, 3488, 4360, 6976, 8720, 17440

Step-4: Factors of 34900

List of positive integer factors of 34900 that divides 34880 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 349, 698, 1396, 1745, 3490, 6980, 8725, 17450

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34880 and 34900. The biggest common factor number is the GCF number.
So the greatest common factor 34880 and 34900 is 20.

Also check out the Least Common Multiple of 34880 and 34900