What is the Greatest Common Factor of 34890 and 34900?

Greatest common factor (GCF) of 34890 and 34900 is 10.

GCF(34890,34900) = 10

We will now calculate the prime factors of 34890 and 34900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34890 and 34900.

How to find the GCF of 34890 and 34900?

We will first find the prime factorization of 34890 and 34900. After we will calculate the factors of 34890 and 34900 and find the biggest common factor number .

Step-1: Prime Factorization of 34890

Prime factors of 34890 are 2, 3, 5, 1163. Prime factorization of 34890 in exponential form is:

34890 = 2¹ × 3¹ × 5¹ × 1163¹

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 34890

List of positive integer factors of 34890 that divides 34890 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 1163, 2326, 3489, 5815, 6978, 11630, 17445

Step-4: Factors of 34900

List of positive integer factors of 34900 that divides 34890 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 34890 and 34900. The biggest common factor number is the GCF number.
So the greatest common factor 34890 and 34900 is 10.

Also check out the Least Common Multiple of 34890 and 34900