3600
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Number
$3600$ (three thousand, six hundred) is:
 $2^4 \times 3^2 \times 5^2$
 The $60$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $2304$, $2401$, $2500$, $2601$, $2704$, $2809$, $2916$, $3025$, $3136$, $3249$, $3364$, $3481$:
 $3600 = 60 \times 60$
 The $49$th positive integer which cannot be expressed as the sum of a square and a prime:
 $1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$, $2209$, $2304$, $2500$, $2809$, $2986$, $3136$, $3364$, $3481$, $3600$, $\ldots$
Arithmetic Functions on $3600$
\(\displaystyle \map \tau { 3600 }\)  \(=\)  \(\displaystyle 45\)  $\tau$ of $3600$ 

Also see
Historical Note
There are $3600$ seconds of time in an hour.
There are $3600$ seconds of arc in an degree.
There are $3600$ minutes of arc in a $60$ degree angle.
These divisions date back to the time of the Babylonians, who used a $60$based number system for their mathematics and astronomy.
Sources
 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $3600$
 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3600$