5040

5040 is a number that appears frequently in various mathematical contexts, particularly in combinatorics and number theory. It is known as the factorial of 7, denoted as 7!, which is the product of all positive integers from 1 to 7. The calculation of 7! is as follows: 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040. This number has 4 digits, making it a four-digit number. In combinatorics, 5040 is significant because it represents the number of permutations of 7 distinct objects. It is also a highly composite number, meaning it has more divisors than any smaller positive integer. The divisors of 5040 include 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 60, 70, 84, 105, 120, 140, 168, 210, 252, 280, 336, 350, 420, 504, 560, 672, 756, 840, 1008, 1260, 1680, 2520, and 5040. This makes 5040 a number of interest in both recreational mathematics and more advanced mathematical studies.