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Vedic maths · trick 36 of 36 · free

HCF by subtraction — Vedic maths trick

Whatever divides two numbers also divides their difference. So you can shrink the numbers by subtracting until the HCF is left — no factor trees.

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The trick

Sankalana-Vyavakalanabhyam — “by addition and by subtraction”

  1. Take the smaller number away from the bigger one, as many times as it goes.
  2. Now use the smaller number and what is left.
  3. Repeat until nothing is left: the last number before 0 is the HCF.

Use it for: HCF of two numbers (Class 5–8), simplifying fractions (trick 33).

Worked example: HCF of 84 and 126 = 42

  1. 126 − 84 = 42. Now use 84 and 42.
  2. 84 − 2 × 42 = 0 — nothing left.
  3. The last number before 0 is 42.
  4. Answer: 42.

Check: 84 = 2 × 42 and 126 = 3 × 42, and 2 and 3 share no factor ✓

▶ Watch it animated

✓ Written and checked by the TalentJR team · Updated 13 Oct 2026 · How we make our lessons

✏️ Practice

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

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🏁 Trick 36 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 🤝 HCF Hero badge when you pass — and a certificate when you finish all 6 tricks of Part 4 · Algebra & number sense. You can still take the test without signing in.

🖨️ HCF Worksheet

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