What is the Greatest Common Factor of 32340 and 32349?

Greatest common factor (GCF) of 32340 and 32349 is 3.

GCF(32340,32349) = 3

We will now calculate the prime factors of 32340 and 32349, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32340 and 32349.

How to find the GCF of 32340 and 32349?

We will first find the prime factorization of 32340 and 32349. After we will calculate the factors of 32340 and 32349 and find the biggest common factor number .

Step-1: Prime Factorization of 32340

Prime factors of 32340 are 2, 3, 5, 7, 11. Prime factorization of 32340 in exponential form is:

32340 = 2² × 3¹ × 5¹ × 7² × 11¹

Step-2: Prime Factorization of 32349

Prime factors of 32349 are 3, 41, 263. Prime factorization of 32349 in exponential form is:

32349 = 3¹ × 41¹ × 263¹

Step-3: Factors of 32340

List of positive integer factors of 32340 that divides 32340 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 14, 15, 20, 21, 22, 28, 30, 33, 35, 42, 44, 49, 55, 60, 66, 70, 77, 84, 98, 105, 110, 132, 140, 147, 154, 165, 196, 210, 220, 231, 245, 294, 308, 330, 385, 420, 462, 490, 539, 588, 660, 735, 770, 924, 980, 1078, 1155, 1470, 1540, 1617, 2156, 2310, 2695, 2940, 3234, 4620, 5390, 6468, 8085, 10780, 16170

Step-4: Factors of 32349

List of positive integer factors of 32349 that divides 32340 without a remainder.

1, 3, 41, 123, 263, 789, 10783

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32340 and 32349. The biggest common factor number is the GCF number.
So the greatest common factor 32340 and 32349 is 3.

Also check out the Least Common Multiple of 32340 and 32349