Respuesta :
The sum of these four positive integers is 12
For given question,
There are four positive integers that are divisors of each number in the list 36, 72, -12, 114, 96
We need to find the sum of these four positive integers.
We will begin by finding all the positive factors of -12, which are the same as the positive factors of 12.
The positive factors of 12 are 1, 2, 3, 4, 6, and 12.
The four numbers we seek must be among these six numbers.
Clearly, the number 4 is not a factor of each number on the list, since dividing 114 by 4 gives a remainder of 2.
We also know that 12 cannot be a factor of 114, since dividing 114 by 12 gives a remainder of 6.
However, 6 is a factor of each number on the list, since,
36 = 6 × 6
72 = 6 × 12
-12 = 6 × (-2)
96 = 6 × 16
114 = 6 × 19
Since 1, 2, 3, and 6 are factors of 6, and 6 is a factor of each number on the list, 1, 2, 3, and 6 must be a factor of each number on the list.
So, the required four positive integers are: 1, 2, 3, 6
The sum of these four positive integers is:
1 + 2 + 3 + 6 = 12
Therefore, the sum of these four positive integers is 12.
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