What is the Greatest Common Factor of 34874 and 34880?

Greatest common factor (GCF) of 34874 and 34880 is 2.

GCF(34874,34880) = 2

We will now calculate the prime factors of 34874 and 34880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34874 and 34880.

How to find the GCF of 34874 and 34880?

We will first find the prime factorization of 34874 and 34880. After we will calculate the factors of 34874 and 34880 and find the biggest common factor number .

Step-1: Prime Factorization of 34874

Prime factors of 34874 are 2, 7, 47, 53. Prime factorization of 34874 in exponential form is:

34874 = 2¹ × 7¹ × 47¹ × 53¹

Step-2: 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-3: Factors of 34874

List of positive integer factors of 34874 that divides 34874 without a remainder.

1, 2, 7, 14, 47, 53, 94, 106, 329, 371, 658, 742, 2491, 4982, 17437

Step-4: Factors of 34880

List of positive integer factors of 34880 that divides 34874 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34874 and 34880. The biggest common factor number is the GCF number.
So the greatest common factor 34874 and 34880 is 2.

Also check out the Least Common Multiple of 34874 and 34880