The proper divisors of 12 are 1, 2, 3, 4 and 6. A proper divisor of an integer $N$ is a positive divisor of $N$ that is less than $N$. What is the sum of the proper divisors of the sum of the proper divisors of 284

  284

Step-by-step explanation:

The proper divisors of 284 are ...

  1, 2, 4, 71, 142

Their sum is 220.

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The proper divisors of 220 are ...

  1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110

Their sum is 284.

The sum of the proper divisors of the sum of the proper divisors of 284 is 284.

Additional comment

For the prime factorization of a number N, the number of divisors (proper and improper) of N is the product of the exponents of the prime factors, each exponent being increased by 1.

Example:

The prime factorization of 220 is 2²·5·11, so the exponents of the prime factors are 2, 1, 1. The number of divisors of 220 is (2+1)(1+1)(1+1) = 12. 11 of those are the proper divisors listed above. The 12th one is 220.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3