What is the Greatest Common Factor of 34860 and 34880?

Greatest common factor (GCF) of 34860 and 34880 is 20.

GCF(34860,34880) = 20

We will now calculate the prime factors of 34860 and 34880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34860 and 34880.

How to find the GCF of 34860 and 34880?

We will first find the prime factorization of 34860 and 34880. After we will calculate the factors of 34860 and 34880 and find the biggest common factor number .

Step-1: Prime Factorization of 34860

Prime factors of 34860 are 2, 3, 5, 7, 83. Prime factorization of 34860 in exponential form is:

34860 = 2² × 3¹ × 5¹ × 7¹ × 83¹

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 34860

List of positive integer factors of 34860 that divides 34860 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 83, 84, 105, 140, 166, 210, 249, 332, 415, 420, 498, 581, 830, 996, 1162, 1245, 1660, 1743, 2324, 2490, 2905, 3486, 4980, 5810, 6972, 8715, 11620, 17430

Step-4: Factors of 34880

List of positive integer factors of 34880 that divides 34860 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 34860 and 34880. The biggest common factor number is the GCF number.
So the greatest common factor 34860 and 34880 is 20.

Also check out the Least Common Multiple of 34860 and 34880