The Tricky 7 Divisibility Test!

Tired of long division to check if a number is divisible by 7? While 2, 3, 5 are easy, 7 often feels like a rebel! Let's conquer it with a simple, mind-bending trick.

Subject: number-theory • Classes: 6–12 • Difficulty: intermediate

The Trick

The 'Double-Subtract' Rule: 1. Take the last digit of the number. 2. Double it ($ \times 2 $). 3. Subtract this doubled value from the rest of the number (the number without its last digit). 4. Repeat steps 1-3 with the new number until you get a small number that you know is or isn't divisible by 7. If the final number is 0 or a multiple of 7, then the original number is divisible by 7. Why it works: This trick is rooted in modular arithmetic. If a number is $10x + y$, we check if $x - 2y$ is divisible by 7. If $x - 2y \equiv 0 \pmod{7}$, then $x \equiv 2y \pmod{7}$. Substituting this into $10x + y$: $10(2y) + y = 20y + y = 21y$. Since $21y$ is always a multiple of 7, the original number must also be!

Study More with GyanAI

GyanAI is a free AI tutor for CBSE students. Ask any question for an instant step-by-step answer. Try GyanAI free.