Page 15 - NUMINO Challenge_D2

Type 1-2 The Number of Continuous 0’s

What is the total number of continuous 0’s at the end of the result when
the following expression is calculated?

1234 100

1 The following shows the number of 2’s and 5’s from the prime factorization
and the number of 0’s at the end of the given numbers. Complete the
table.

Number Prime Number of 2’s Number of 5’s Number of 0’s at
10 Factorization 1 1 the End
100 2
25 1
1000 2255
200
250

2 Explain the pattern between the number of 2’s or 5’ s and the number of
0’s at the end of the number by looking at the table from 1 .

3 In the multiplication of numbers from 1 to 100, 5 is being multiplied fewer
times than 2. Therefore, you can find the number of 0’ s at the end of the
result if you know how many times 5 is being multiplied. From 1 to 100,
what is the total number of multiples of 5?

4 5 is multiplied twice in the multiples of 25. Therefore, 5 is multiplied one
more time than other multiples of 5. How many multiples of 25 are there
from 1 to 100?

5 How many times 5 is multiplied in the given expression?

6 What is the total number of continuous 0’ s at the end of the result when
the given expression is calculated?

12 NUMINO Challenge D2