# Number Gossip

(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)

## Unique Properties of 248

- 248 is the smallest 3-digit numbers with distinct digits greater than one, such that it is divisible by all of its digits
- 248 is the smallest number n, greater than 1, for which the arithmetic, geometric, and harmonic means of φ(n) and σ(n) are all integers (φ(248) = 120 and σ(248) = 480; there arithmetic, geometric and harmonic means are integers: 300, 240, and 192)
- 248 is the dimension of E
_{8}, the largest exceptional simple Lie algebra (submitted by Qiaochu Yuan)