The number 343264 is divisible by:

The correct option is 32.

To determine which of the given options (43, 32, 29, 27) divides the number 343264 completely, let us test the divisibility of 343264 by checking the options step-by-step.

First, let us check divisibility by 32 using the divisibility rule for powers of 2.
Since $2^5=32$, a number is divisible by 32 if the number formed by its last 5 digits is divisible by 32.

The last 5 digits of 343264 form the number 43264.

Let us perform the long division of 43264 by 32:

$43264÷32$

1. Divide 43 by 32:
$32\times 1=32$
Remainder = $43-32=11$

2. Bring down 2 to make 112:
$32\times 3=96$
Remainder = $112-96=16$

3. Bring down 6 to make 166:
$32\times 5=160$
Remainder = $166-160=6$

4. Bring down 4 to make 64:
$32\times 2=64$
Remainder = $64-64=0$

Since 43264 is completely divisible by 32 (giving a quotient of 1352 with 0 remainder), the original number 343264 is also completely divisible by 32.

Dividing the full number directly:
$343264÷32=10727$

Thus, 343264 is divisible by 32.