# 65,536

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## Number

$65 \, 536$ (sixty-five thousand, five hundred and thirty-six) is:

$2^{16}$

The only known power of $2$ whose digits do not contain $1$, $2$, $4$ or $8$.

The actual number of bytes in $64 \, \mathrm{KB}$ of computer memory.

The $4$th eighth power after $1$, $256$, $6561$:
$65 \, 536 = 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4$

The $4$th power of $16$ after $(1)$, $16$, $256$, $4096$:
$65 \, 536 = 16^4$

The $8$th power of $4$ after $(1)$, $4$, $16$, $64$, $256$, $1024$, $4096$, $16 \, 384$:
$65 \, 536 = 4^8$

The $16$th fourth power after $1$, $16$, $81$, $256$, $625$, $1296$, $2401$, $4096$, $6561$, $10 \, 000$, $14 \, 641$, $20 \, 736$, $28 \, 561$, $38 \, 416$, $50 \, 625$:
$65 \, 536 = 16 \times 16 \times 16 \times 16$

The $16$th power of $2$ after $(1)$, $2$, $4$, $8$, $16$, $32$, $64$, $128$, $256$, $512$, $1024$, $2048$, $4096$, $8192$, $16 \, 384$, $32 \, 768$:
$65 \, 536 = 2^{16}$

The $17$th almost perfect number after $1$, $2$, $4$, $8$, $16$, $32$, $64$, $128$, $256$, $512$, $1024$, $2048$, $4096$, $8192$, $16 \, 384$, $32 \, 768$:
$\map {\sigma_1} {65 \, 536} = 131 \, 071 = 2 \times 65 \, 536 - 1$

The $256$th square number:
$65 \, 536 = 256 \times 256$