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Recognizing the beauty in mathematics and puzzles.

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Divisibility Tests from 2 to 10 Explained with Modular Arithmetic

The Mathematics Behind Everyday Divisibility Rules

12 min readOct 20, 2026

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Welcome to my Number Theory Series!

Join me as we explore the captivating world of numbers, from primes and divisibility to hidden patterns, elegant proofs, thought-provoking questions, and unsolved conjectures. Together, we’ll uncover the beauty of mathematics, one number at a time.

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Have you ever wondered how we can determine whether a large number is divisible by 9 without performing long division ? Or why checking just the last two digits is enough to test divisibility by 4 ?

I find these shortcuts fascinating because they reveal something deeper than mental arithmetic. Behind each rule lies a mathematical structure that explains exactly why it works.

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Thanushan Sivapatham
Thanushan Sivapatham

Written by Thanushan Sivapatham

𝐍𝐮𝐦𝐛𝐞𝐫 𝐄𝐧𝐭𝐡𝐮𝐬𝐢𝐚𝐬𝐭 🤓 || Tips : https://ko-fi.com/thanushan23

ThinkArt
ThinkArt

Published in ThinkArt

Recognizing the beauty in mathematics and puzzles.