All multiples of 5 are numbers ending in either 5 or 0.
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Multiples of 2 are: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30 simply adding 2 multiples of 5 are: 5,10,15,20,25,30 simply adding 5 multiples of 2 and 5 are the ones that are common between the two. some of them would include 10,20,30,40,50,60,70,80,90,100
The factors of 35 are 1, 5, 7, and 35. Multiples of 35 are 35, 70, 105, 140,...etc.
hmm, 3,6,9,12,15 maybe
There are 2000 4-digit numbers that are multiples of 5, so, instead of listing them all, it is equally valid to say: Any4-digit number whose final digit is either a 5 or a 0 is a multiple of 5. Get Right? :P
The question, as asked, is difficult to answer, The number of zeros in factorial 100 is not the same as the number of 0s at the end of factorial 100 since there will be some before the end.The answer to the second question is easy:The number of zeros is determined by the number of 10s in the factors.Since 2s are common, this, in turn, depends on the number of 5s.In 100!, there are 20 multiples of 5 each of which will contribute a 5 to the factors of 100!.In addition there are 4 multiples of 52 = 25 each of which will contribute another 5 to the factors of 100!All in all, therefore, there are 24 5s giving 24 0s at the end of 100!