SOLUTION: Let P denote the product of all the positive primes less than 100. What is the units' digit of P? ----------- ----------- ----------- ---- I started writing out the primes from

Algebra ->  Equations -> SOLUTION: Let P denote the product of all the positive primes less than 100. What is the units' digit of P? ----------- ----------- ----------- ---- I started writing out the primes from      Log On


   

Question 73701: Let P denote the product of all the positive primes less than 100. What is the units' digit of P?
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I started writing out the primes from 1 to 99, but it took forever and I missed a lot of them. There must be some way to get this answer WITHOUT doing all that math, right?
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
You got it ... there's an easy way once you think about it a little. But before that, there are
25 prime numbers between 1 and 100. They are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,
43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
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Let's look at the product of just two of these primes. The product of 2 and 5 is, of course,
10. After that, what is the units digit of any other multiplication? 10 * 3 = 30. That times
7 is 210. Times 11 is 2310. There we have the product of the first 5 primes. And by now you
can probably see that any additional multiplications will end in zero in the units position (even if you go to the product of the primes out to a million or beyond).
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Does this help? Hope so ...