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The Question of the Day - 15 points

Lucky Prime Hint! I am a 2-digit prime number that is not divisible by 4 or 7.

How many even positive integral factors does 84,000,000 have? Calculators are permitted for this question, although it is easily solvable without one.

Previous Solution

The lucky prime was 853. Note that I create the lucky prime before I see the answers you wrote. This is not biased in any way.

The answer to yesterday's question was 225.

Solution to yesterday's question:

From 100 to 199, there are 18 numbers that have exactly one 8 as one of their digits. (There are ten that have an 8 in the tens place 80-89 and ten that have an 8 in the units place 108, 118, 198. That would be 20 numbers, except that 188 would be counted twice when we don't want to count it at all since it doesn't have exactly one 8, so only 18 since we counted a number twice that we didn't want to count at all.) There will also be 18 numbers in the 200s, 300s, 400s, 500s, 600s, 700s, and 900s. In the 800s, all the numbers have at least one 8, but 19 of the numbers have an additional 8, so only 81 that have exactly one 8. That is a total of 18*8+81=25


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