Divisibility tests — Vedic maths trick

The trick

Ekadhikena Purvena — “by one more than the one before (the osculator)”

1. 2, 5, 10: the last digit (even; 0 or 5; 0). 3 and 9: add the digits. 4: the last two digits. 8: the last three digits. 6: even and passes the rule for 3.
2. 11: from the right, add the 1st, 3rd, 5th… digits and the 2nd, 4th… digits; the difference must be 0 or a multiple of 11.
3. Any prime p: multiply p by 1, 3, 7 or 9 so it ends in 9; one more than the digits before the 9 is the osculator (7 → 5, 13 → 4, 17 → 12, 19 → 2, 23 → 7, 29 → 3).
4. Take the last digit × the osculator and add it to the rest; repeat until the number is small and check the times table.
5. Composite numbers: split into two factors that share no factor and pass BOTH rules — 6 = 2 × 3, 12 = 3 × 4, 15 = 3 × 5, 18 = 2 × 9, 20 = 4 × 5, 24 = 3 × 8, 30 = 3 × 10.

Use it for: Simplifying fractions, finding factors, HCF and LCM, and checking division answers.

Worked example: Is 3157 divisible by 7? Yes

✏️ Practice

Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.

🏁 Trick 13 test

20 sums. Check each answer, then go to the next one. Get 16 or more right to pass.

🏅 Sign in with Google to earn the 🔑 Divisibility Key badge when you pass — and a certificate when you finish all 10 tricks of Part 2 · Advanced tricks. You can still take the test without signing in.

🖨️ Divisibility Rules Worksheet

• Worksheet set 1 (PDF)
• Worksheet set 2 (PDF)
• Worksheet set 3 (PDF)