They advance from 5 x 101=505 to 5 x 200=1000.
Oh, dude, let me break it down for you. So, the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Out of these, the multiples of 5 are 5, 10, 20, 25, 50, and 100. That's like 6 factors of 100 that are multiples of 5. Easy peasy, lemon squeezy!
The multiples of 5 that are also multiples of 6 are multiples of their LCM. The LCM of 5 and 6 is 30, so the question becomes which multiples of 30 are less than 100? The solution is the numbers: 30, 60, 90
Multiples of 5 include 5, 10 and 15. For them to be common, they need to be compared to another set of multiples.
20
20,40,60,80,and 100
5,10,15,20,25,30,35,40,45,50,55,60
There are an infinite number of multiples of 100. 100, 200, 300,400, ....
5, 10, 15 and just keep adding 5 until you get to 100.
100, 200, 300, 400, 500.
If 100-300 is inclusive, the answer is 41.
100, 200, 300, 400, 500
The highest power of 25 that divides the product of the first 100 multiples of 5 is 50. This is because for each multiple of 25, we have an extra factor of 25. Since there are 4 multiples of 25 in the first 100 multiples of 5, we have a total of 50 factors of 25.