Producing Zeros
Weekly Problem 10 - 2008
If the numbers 1 to 10 are all multiplied together, how many zeros are at the end of the answer?
If the numbers 1 to 10 are all multiplied together, how many zeros are at the end of the answer?
Age
11 to 14
Challenge level
Problem
If the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 are all multiplied together, how many zeros are there at the end of the answer?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: Two zeros
You could write this problem out as $1\times3\times4\times6\times7\times8\times9\times(2\times5)\times10$. The product of the first seven numbers is not a multiple of ten, but the last part gives us $10\times10$ so the overall product must be a multiple of $100$, but not a multiple of $1000$. So the answer is two zeros.