Sub-Sūtra 2 of 13

Śiṣyate Śeṣasaṁjñaḥ

The remainder remains

Quick divisibility tests using remainders.

When to use

Modular arithmetic, divisibility checks.

How it works

Reduce a large number's remainder modulo n by repeatedly summing transformed digits.

Memory formula

Only the remainder matters; keep reducing until the answer is obvious.

Worked examples

Problem 1

Is 12345 divisible by 9?

0/3

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