The Secret to Divisibility by 7
Divisibility by 2, 3, 5, 10 are easy. But what about 7? It often feels like the odd one out! Unravel the mystery of checking divisibility by 7 with this neat trick!
Subject: number-theory • Classes: 6–12 • Difficulty: intermediate
The Trick
To check if a number is divisible by 7: 1. Take the last digit of the number. 2. Double it. 3. Subtract this doubled value from the rest of the number (the number without its last digit). 4. If the result is 0 or a number divisible by 7, then the original number is divisible by 7. Repeat if the result is still a large number. **Why it works:** Let the number be $10a + b$, where $b$ is the last digit and $a$ is the preceding digits. If $a - 2b$ is divisible by 7, let $a - 2b = 7k$. Then $a = 7k + 2b$. Substitute $a$ back into the original number: $10(7k + 2b) + b = 70k + 20b + b = 70k + 21b = 7(10k + 3b)$. Since the original number can be written as $7 \times (\text{an integer})$, it must be divisible by 7.
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.