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In other words, any integer is divisible by all of its factors— and it is also divisible by all of the factors of its factors. For example, if 72 is divisible by 12, then 72 is also divisible by all the factors of 12 1, 2, 3, 4, 6, and Written another way, if 12 is a factor of 72, then all the factors of 12 are also factors of The number 12, in turn, is built from its own factors; for example, 4 x 3 builds Thus, if 12 is part of the foundation of 72 and 12 in turn rests on the foundation built by its prime factors 2, 2, and 3 , then 72 is also built on the foundation of 2, 2, and 3.
We say almost any factor, because one of the factors cannot be built out of the building blocks in the foundation: the number 1. Remember that the number 1 is not prime, but it is still a factor of every integer.
Except for the number 1, every factor of 72 can be built out of the lowest level of 72 building blocks. A Prime Box is exactly what its name implies: a box that holds all the prime factors of a number in other words, the lowest-level building blocks. Here are prime boxes for 72, 12, and 72 12 2, 2, 2, 3,3 Notice that you must repeat copies of the prime factors if the number has multiple copies of that prime factor.
You can use the prime box to test whether or not a specific number is a factor of another number. Is 27 a factor of 72? But you can see that 72 only has two 3 s in its prime box.
Therefore you cannot make 27 from the prime factors of Thus, 27 is not a factor of Given that the integer n is divisible by 3,7, and 11, what other numbers must be divisors of n? Without even knowing what n is, you have found 4 more of its factors: 21, 33, 77, and This reminds you that you have created a partial prime box of n.
Whereas the complete set of prime factors of 72 can be calculated and put into its prime box, you only have a partial list of prime factors of n, because n is an unknown number.
You know that n is divisible by 3, 7, and 11, but you do not know what additional primes, if any, n has in its prime box.
Most of the time, when building a prime box for a variable, you will use a partial prime box, but when building a prime box for a number, you will use a complete prime box.
Urban areas such as New York City are especially vulnerable to temperature extremes due to the high concentration of susceptible populations 5 , as well as enhancement of temperatures due to the urban heat island effects 6.
Several studies have projected future heat-related mortality resulting from climate change 9 , 10 , 11 , 12 , 13 , These studies follow a health impact assessment HIA approach, integrating temperature projections from global-scale climate models with empirical exposure-response relationships from the epidemiologic literature. While most HIAs for climate change have focused on heat-related mortality, decreasing cold-related mortality may also be important A growing number of studies have examined seasonal mortality tradeoffs in a changing climate 16 , 17 , 18 , 19 , 20 , 21 , However, results have been difficult to compare due to differences in health and climate modeling methods.
The objective of the present study was to project future temperature-related mortality impacts over the full year for the NYC borough of Manhattan New York County across a broad range of statistically downscaled climate models and greenhouse gas emissions scenarios in the s, s and s. Fitted spline functions relating percent increase in daily mortality to daily Tmax in degrees F using historical data are displayed graphically in Figure 1.
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