Not a Zero
What is the last non-zero digit of $2^{57} \times 3^4 \times 5^{53}$?
Age
11 to 14
Challenge level
Problem
What is the last non-zero digit of $2^{57} \times 3^4 \times 5^{53}$?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: $6$
The zeros on the end of the number are caused by factors of $10$.
$2^{57} \times 3^4 \times 5^{53} = 2^4 \times 3^4 \times 2^{53} \times 5^{53} = 2^4 \times 3^4 \times 10^{53} = 6^4\times10^{53}$
Last non-zero digit comes from $6^4$
$6^1=6$
$6^2=36$
$6^3=\ ...6$
$6^4=\ ...6$
This means the last non-zero digit will be a $6$.