Question

the sum of all the factors of a positive number 'k' greater than 1 is 'p'. which of these could be the ratio of 'p' to 'k'?​

Answer 1

Given :  The sum of all the factors of a positive number 'k' greater than 1 is 'p'.

To Find  : Which of these could be the ratio of ‘p’ to ‘k’ ?

A) 2 : 5

B) 6 : 5

C) 3 : 7

D) 1 : 1

Solution :

k >  1

Hence k has at least   2 factors  1   and  k

Sum of  all  factors   ≥   k + 1

The sum of all the factors = p

=> p  ≥   k  +  1

=> p/k  ≥   1  + 1/k

2 : 5  => 2/5  =    1   - 3/5  does not satisfy  1  + 1/k

6 : 5  => 6/5  = 1  + 1/5    satisfy  1  + 1/k

3 : 7 => 3/7  = 1  - 4/7  does not satisfy  1  + 1/k

1 : 1  =>  1 /1  =  1         does not satisfy  1  + 1/k

Hence  ratio of ‘p’ to ‘k’  can  be   6 : 5  in the given options

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Answer 2

Step-by-step explanation:

___________originated from the province of Sorsogon. from

Sorsogon, officially the Province of Sorsogon is a province in the Philippines