Discover the logic behind divisibility rules and number puzzles built around place value.
Divisibility rules let you check if a number divides evenly without doing long division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3, and by 9 if the digit sum is divisible by 9.
Is 4581 divisible by 3?
4+5+8+1 = 18, which is divisible by 3, so yes
Is 2394 divisible by 9?
2+3+9+4 = 18, which is divisible by 9, so yes
Many number puzzles rely on understanding place value — for instance, a 2-digit number can be written as 10×(tens digit) + (units digit), which helps solve problems about reversing or swapping digits.
A 2-digit number has digit sum 9. If the digits are reversed, the new number is 27 more than the original. Find the number.
Let tens digit = a, units digit = b. a+b=9, and (10b+a) − (10a+b) = 27, giving 9(b−a) = 27, so b−a = 3. Solving: a=3, b=6, number is 36
Why can a 3-digit number and its digit-reversed version always be evenly divided by 99 when their difference is taken (if the hundreds and units digits differ)?
Because reversing swaps the hundreds and units place, and the difference works out to a multiple of 99 due to how place values (100 and 1) relate
1. Is 6342 divisible by 3?
2. Is 5184 divisible by 9?
3. Is 7212 divisible by 4? (Hint: check the last two digits)
4. A 2-digit number has digit sum 11. If the digits are reversed, the new number is 45 more than the original. Find the number.
5. Is 9000 divisible by 6? (Hint: check divisibility by both 2 and 3)