What is the Greatest Common Factor of 45904 and 45920?

Greatest common factor (GCF) of 45904 and 45920 is 16.

GCF(45904,45920) = 16

We will now calculate the prime factors of 45904 and 45920, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45904 and 45920.

How to find the GCF of 45904 and 45920?

We will first find the prime factorization of 45904 and 45920. After we will calculate the factors of 45904 and 45920 and find the biggest common factor number .

Step-1: Prime Factorization of 45904

Prime factors of 45904 are 2, 19, 151. Prime factorization of 45904 in exponential form is:

45904 = 2⁴ × 19¹ × 151¹

Step-2: Prime Factorization of 45920

Prime factors of 45920 are 2, 5, 7, 41. Prime factorization of 45920 in exponential form is:

45920 = 2⁵ × 5¹ × 7¹ × 41¹

Step-3: Factors of 45904

List of positive integer factors of 45904 that divides 45904 without a remainder.

1, 2, 4, 8, 16, 19, 38, 76, 151, 152, 302, 304, 604, 1208, 2416, 2869, 5738, 11476, 22952

Step-4: Factors of 45920

List of positive integer factors of 45920 that divides 45904 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 32, 35, 40, 41, 56, 70, 80, 82, 112, 140, 160, 164, 205, 224, 280, 287, 328, 410, 560, 574, 656, 820, 1120, 1148, 1312, 1435, 1640, 2296, 2870, 3280, 4592, 5740, 6560, 9184, 11480, 22960

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45904 and 45920. The biggest common factor number is the GCF number.
So the greatest common factor 45904 and 45920 is 16.

Also check out the Least Common Multiple of 45904 and 45920