How many 0 continues from the place of one, as for the product multiplied by the integers from 1 to 40?
Since 10 = 2 × 5, check the numbers both of multiples of 2 and 5 in 1-40.
There are more numbers of multiple of 2 than the multiple of 5.
Then counts how many multiples of 5 are in 1-40.
Since 40/5=8, there are eight pieces.
Furthermore since 25 = 5 × 5, the number of multiple of 25 should be also counted, it is one by calculation 40/25=1 remainder 15.
It turns out that there are 8 + 1 = 9 pieces in total.
Therefore, nine 0 continues from the place of one in the product.
Nine
Solution
It is checked how many times the product obtained by multiplying from 1 to 40 can be divided by 10.
Since 10 = 2 × 5, check the numbers both of multiples of 2 and 5 in 1-40.
There are more numbers of multiple of 2 than the multiple of 5.
Then counts how many multiples of 5 are in 1-40.
Since 40/5=8, there are eight pieces.
Furthermore since 25 = 5 × 5, the number of multiple of 25 should be also counted, it is one by calculation 40/25=1 remainder 15.
It turns out that there are 8 + 1 = 9 pieces in total.
Therefore, nine 0 continues from the place of one in the product.
