answersLogoWhite

0


Best Answer

The answer is 3.25 or 13/4 First, notice that if you multiply the reciprocal of a divisor by 360, it's the same as dividing 360 by the divisor, so you get another divisor of 360. This means that if we multiply the sum we want by 360, each reciprocal-of-a-divisor becomes a divisor, and we get the sum of divisors of 360. This is far easier to calculate, so we'll find the sum of the divisors first, and then divide by 360. The prime factorization of 360 is 2*2*2*3*3*5, so the divisors are: 1, 2, 2*2, 2*2*2,

3, 2*3, 2*2*3, 2*2*2*3,

3*3, 2*3*3, 2*2*3*3, 2*2*2*3*3,

5, 2*5, 2*2*5, 2*2*2*5,

3*5, 2*3*5, 2*2*3*5, 2*2*2*3*5,

3*3*5, 2*3*3*5, 2*2*3*3*5, 2*2*2*3*3*5.

The way I have grouped them is for a reason. First, the second group is 5 times the first group, so the sum of the divisors is (1+5) times the first group. Second, in the first group, the second row is 3 times the first, and the third row is 9 times the first, so the sum of the first group is (1+3+9) times the first row. Finally, the sum of the first row is (1+2+4+8). So the sum of all the divisors is (1+5)(1+3+9)(1+2+4+8) = 6*13*15 = 1170. Now to get our final answer we have to divide by 360, getting 3.25. Of course, we could also get the answer by listing all the reciprocals and adding them. But this method works exactly the same way for any number, provided you can factor it. ----------------------------------------- New Question ---------------------------------------------- How would we get the fraction 360/1170 in this problem?

User Avatar

Wiki User

โˆ™ 2008-11-16 23:32:44
This answer is:
๐Ÿ™
0
๐Ÿคจ
0
๐Ÿ˜ฎ
0
User Avatar
Study guides

Algebra

20 cards

A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common factor A True B False

The sum or difference of p and q is the of the x-term in the trinomial

A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

โžก๏ธ
See all cards
3.71
โ˜†โ˜…โ˜†โ˜…โ˜†โ˜…โ˜†โ˜…โ˜†โ˜…
364 Reviews
More answers
User Avatar

Anonymous

Lvl 1
โˆ™ 2020-04-20 11:37:17

71/30

User Avatar

Add your answer:

Earn +20 pts
Q: What is the sum of the reciprocals of the divisors of 360?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

What is the sum of the reciprocals of the divisors of 360 if the divisors of 360 add up to 1170?

1170 over 360 or 13 over 4


What is the sum of the reciprocals of all the divisors of 6 is?

2


What is the sum of the divisors of 1034?

Sum of divisors: 1728.


What is the sum of the divisors of 1211?

Sum of divisors: 1,392.


What is the sum of the divisors of 556?

Sum of divisors: 980.


What is the sum of the divisors of 36?

Sum of divisors = 91.


Is the sum of the reciprocals 1?

No, the product of reciprocals is 1.


What is the sum of the divisors of 130?

Sum of divisors of 130 = 252.


What is the sum of the divisors of 24?

Sum of 24's divisors: 60.


What is the sum of the divisors of 150?

Sum of 150's divisors = 372.


The sum of two numbers is 10 their product is 20 the sum of reciprocals is what?

It is 0.5


What is the sum of all the positive divisors of 72?

The sum is 195.


What is a perfect Abundant Or dificient number?

A perfect number equals the sum of its proper divisors. A deficient number is greater than the sum of its proper divisors. An abundant number is less than the sum of its proper divisors. Proper divisors of a number do not include the number itself.


Determine the sum of the reciprocals of the two number which are their sum is 2 and their product is 3?

sannie


What are the proper divisors of 24 and the sum of these divisors?

1, 2, 3, 4, 6, 8, 12, 24 (sum = 60)


What is the smallest number with 24 divisors?

360


What is the sum of all divisors of 100?

its 217


What is the sum of all the divisors of 24?

60


Can the sum of the reciprocals of two positives numvers is equal to the reciprocal of their sum?

No. That only works with products.


How do you calculate total capacitance if connected in series?

reciprocal of the sum of the reciprocals.


Is 8 a perfect number?

A perfect number is the sum of its divisors; for example 6 is a perfect number because the sum of its divisors is 6 (1 + 2 + 3). The sum of the divisors of 8 is 7 (1 + 2 + 4), so 8 is not a perfect number.


The sum of the reciprocals of three prime numbers is 167 over 285 What is the sum of the three prime numbers?

27


If the sum of two numbers is 7 and there product is 25 what is the sum of there reciprocals?

Suppose the two numbers are x and y. Then, the sum of THEIR reciprocals is 1/x + 1/y = y/xy + x/xy = (y + x)/xy = 7/25


What is the sum of the divisors of the first eleven positive integers?

99


What is the sum of all the whole number divisors of 8?

15