720 (number)
720 is a natural number following 719 and preceding 721. It is a composite number with a significant number of factors and interesting mathematical properties.
Properties:
- Factorization: 720 can be prime factorized as 24 * 32 * 5.
- Number of Divisors: It has 30 divisors (including 1 and itself).
- Highly Composite Number: 720 is a highly composite number, meaning it has more divisors than any smaller positive integer.
- Divisors: The divisors of 720 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720.
- Factorial Relation: 720 is equal to 6! (6 factorial), meaning 6 * 5 * 4 * 3 * 2 * 1 = 720. This connection makes it significant in combinatorics and permutation calculations.
- Geometric Significance: It can be related to geometric shapes and angles, often arising in calculations involving polygons or rotations.
- Practical Applications: 720 is commonly found in scenarios involving combinations, permutations, and arrangements due to its factorial relationship and large number of divisors. For instance, it appears in calculating the number of ways to arrange 6 distinct objects.