What is the Greatest Common Factor of 38514 and 38523?

Greatest common factor (GCF) of 38514 and 38523 is 3.

GCF(38514,38523) = 3

We will now calculate the prime factors of 38514 and 38523, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38514 and 38523.

How to find the GCF of 38514 and 38523?

We will first find the prime factorization of 38514 and 38523. After we will calculate the factors of 38514 and 38523 and find the biggest common factor number .

Step-1: Prime Factorization of 38514

Prime factors of 38514 are 2, 3, 7, 131. Prime factorization of 38514 in exponential form is:

38514 = 2¹ × 3¹ × 7² × 131¹

Step-2: Prime Factorization of 38523

Prime factors of 38523 are 3, 12841. Prime factorization of 38523 in exponential form is:

38523 = 3¹ × 12841¹

Step-3: Factors of 38514

List of positive integer factors of 38514 that divides 38514 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 131, 147, 262, 294, 393, 786, 917, 1834, 2751, 5502, 6419, 12838, 19257

Step-4: Factors of 38523

List of positive integer factors of 38523 that divides 38514 without a remainder.

1, 3, 12841

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38514 and 38523. The biggest common factor number is the GCF number.
So the greatest common factor 38514 and 38523 is 3.

Also check out the Least Common Multiple of 38514 and 38523