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Sometimes the number 1 is included in the proper factors, and sometimes it is not. In the list of factors I have included the number 1. The following numbers have 10 or 11 proper factors, depending on whether 1 is allowed as a proper factor.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36.
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42.
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45.
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48.
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Why cant a negative integer be greater than a positive integer?
By definition, a negative integer is any integer less than zero. Similarly, a positive integer is any integer greater than zero. It should be immediately obvious that an integer cannot be both less than and greater than zero. Therefore, a negative integer cannot be greater than a positive integer.
What is the largest positive integer less than 10?
9
What is the largest positive integer less than 5?
4
When is then product of a negative integer and a positive integer less than both of its factors?
This is a clever question. I would say: "Always". To be more precise: The product is never greater than either factor, and if neither factor is ' 1 ', then the product is always less than both.
What is the greatest possible length of a positive integer less that 1000?
The greatest possible 'length' comes from the number with the greatest number of prime factors. The greatest number of factors is created by using the smallest prime number, 2, as a factor as many times as possible. Since 2^9=512 and 2^10=1024, the greatest possible 'length' of a positive integer less than 1000 is 9.
