**The Block Split Method**

To derive the test of divisibility for n (a natural number), say we have this relation –

Let us take a natural number . When will ? –

*Interpret *the number taken this way –

$latex a_{l}a_{l-1}\hdots a_2a_1= x\cdot 10^r +y$

If,

So we are done if the last congruence relation alone is checked.

Let us try applying this for certain simple cases –

*Check for divisibility for 1001*

Note that

Let the number be

*Interpret* the number as –

$latex 1001p + q – p$

Thus, essentially we can check the divisibility of the number XYZABC by checking the same for – .

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