What is the Greatest Common Factor of 65754 and 65772?

Greatest common factor (GCF) of 65754 and 65772 is 18.

GCF(65754,65772) = 18

We will now calculate the prime factors of 65754 and 65772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 65754 and 65772.

How to find the GCF of 65754 and 65772?

We will first find the prime factorization of 65754 and 65772. After we will calculate the factors of 65754 and 65772 and find the biggest common factor number .

Step-1: Prime Factorization of 65754

Prime factors of 65754 are 2, 3, 13, 281. Prime factorization of 65754 in exponential form is:

65754 = 2¹ × 3² × 13¹ × 281¹

Step-2: Prime Factorization of 65772

Prime factors of 65772 are 2, 3, 7, 29. Prime factorization of 65772 in exponential form is:

65772 = 2² × 3⁴ × 7¹ × 29¹

Step-3: Factors of 65754

List of positive integer factors of 65754 that divides 65754 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234, 281, 562, 843, 1686, 2529, 3653, 5058, 7306, 10959, 21918, 32877

Step-4: Factors of 65772

List of positive integer factors of 65772 that divides 65754 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 27, 28, 29, 36, 42, 54, 58, 63, 81, 84, 87, 108, 116, 126, 162, 174, 189, 203, 252, 261, 324, 348, 378, 406, 522, 567, 609, 756, 783, 812, 1044, 1134, 1218, 1566, 1827, 2268, 2349, 2436, 3132, 3654, 4698, 5481, 7308, 9396, 10962, 16443, 21924, 32886

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 65754 and 65772. The biggest common factor number is the GCF number.
So the greatest common factor 65754 and 65772 is 18.

Also check out the Least Common Multiple of 65754 and 65772