What is the Greatest Common Factor of 38346 and 38360?

Greatest common factor (GCF) of 38346 and 38360 is 14.

GCF(38346,38360) = 14

We will now calculate the prime factors of 38346 and 38360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38346 and 38360.

How to find the GCF of 38346 and 38360?

We will first find the prime factorization of 38346 and 38360. After we will calculate the factors of 38346 and 38360 and find the biggest common factor number .

Step-1: Prime Factorization of 38346

Prime factors of 38346 are 2, 3, 7, 11, 83. Prime factorization of 38346 in exponential form is:

38346 = 2¹ × 3¹ × 7¹ × 11¹ × 83¹

Step-2: Prime Factorization of 38360

Prime factors of 38360 are 2, 5, 7, 137. Prime factorization of 38360 in exponential form is:

38360 = 2³ × 5¹ × 7¹ × 137¹

Step-3: Factors of 38346

List of positive integer factors of 38346 that divides 38346 without a remainder.

1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 83, 154, 166, 231, 249, 462, 498, 581, 913, 1162, 1743, 1826, 2739, 3486, 5478, 6391, 12782, 19173

Step-4: Factors of 38360

List of positive integer factors of 38360 that divides 38346 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 137, 140, 274, 280, 548, 685, 959, 1096, 1370, 1918, 2740, 3836, 4795, 5480, 7672, 9590, 19180

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38346 and 38360. The biggest common factor number is the GCF number.
So the greatest common factor 38346 and 38360 is 14.

Also check out the Least Common Multiple of 38346 and 38360