Number Sense

From Washington State 1996 Math Olympiad sponsored by WSMC
1). (2 points) The number 12 has six factors: 1, 2, 3, 4, 6, and 12. This is an even number of factors for the number 12. Which numbers between 0 and 20 have an odd number of factors?




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2). (3 points) how many distinct, whole number factors does 720 have?


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3). (3 points) A football team boasts that all the numbers on their jerseys are prime numbers under 100. What is the largest number of players the team could have?


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4). (3 points) Ken has between 3 and 100 seashells in his collection. If he counts his sea shells 3 at a time, he has 2 left over. If he counts them 4 at a time he has 2 left over. If he counts them 5 at a time, he has 2 left over! How many seashells does Ken have?


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5). (3 points) Find 6 three digit numbers, each less than 300, where each number is exactly divisible by 6 and where the sum of the digits of each number is 6.


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