As you increase the units digit of alternates between 1 and 9. Why? Because for arbitrary digitswhat is the units digit of 9^4321 power?
which has a units digit of 1, and it can be similarly shown that any integer ending in 1, when multiplied by 9, will give an integer ending in 9 (because ).
So, for even ends in a 1, and for odd ends in a 9. We have the odd case, so the units digit is nine.
Bob repairs roofs at a rate of and Frank repairs at a rate of Now, assuming these two slouches don't know the meaning of the word "synergy," their combined repair rate isIf Bob spends 4 hours to completely repair a roof, and Frank spends 6 hours to completely repair that same roof, how long would it take them to repair the roof together.
Thus, to repair this one roof, Bob and Frank will need to work for
This is also a pretty standard problem. The number of zeros corresponds to the number of factors of 10, which is the number of pairs of 2 and 5 in the number's factorization. In every second number in this factorial is even (divisible by two), but only every fifth factor is divisible by five. So, since there are plenty of 2's, the number of factors of 10 is limited only by the factors of 5.How many terminating zeros are in 4321!
so there are 864 numbers between 1 and 4321 that have at least one factor of 5. Similarly, which means that 172 of these numbers also have a second factor of 5. Continuing in this way, the total of number of factors of 5 is
So, there are 1077 trailing zeros.