What is the Greatest Common Factor of 46305 and 46320?

Greatest common factor (GCF) of 46305 and 46320 is 15.

GCF(46305,46320) = 15

We will now calculate the prime factors of 46305 and 46320, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 46305 and 46320.

How to find the GCF of 46305 and 46320?

We will first find the prime factorization of 46305 and 46320. After we will calculate the factors of 46305 and 46320 and find the biggest common factor number .

Step-1: Prime Factorization of 46305

Prime factors of 46305 are 3, 5, 7. Prime factorization of 46305 in exponential form is:

46305 = 3³ × 5¹ × 7³

Step-2: Prime Factorization of 46320

Prime factors of 46320 are 2, 3, 5, 193. Prime factorization of 46320 in exponential form is:

46320 = 2⁴ × 3¹ × 5¹ × 193¹

Step-3: Factors of 46305

List of positive integer factors of 46305 that divides 46305 without a remainder.

1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 49, 63, 105, 135, 147, 189, 245, 315, 343, 441, 735, 945, 1029, 1323, 1715, 2205, 3087, 5145, 6615, 9261, 15435

Step-4: Factors of 46320

List of positive integer factors of 46320 that divides 46305 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 193, 240, 386, 579, 772, 965, 1158, 1544, 1930, 2316, 2895, 3088, 3860, 4632, 5790, 7720, 9264, 11580, 15440, 23160

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 46305 and 46320. The biggest common factor number is the GCF number.
So the greatest common factor 46305 and 46320 is 15.

Also check out the Least Common Multiple of 46305 and 46320