Question

What is the sum of the reciprocals of the positive integer factors of 28?

Answer 1

Answer: 2

Step-by-step explanation: The factors of 28 are 1, 2, 4, 7, 14, and 28.

1/1 + 1/2 + 1/4 + 1/7 +1/14 + 1/28 = 2.

A fun fact of 28 is that it is actually a perfect number, meaning that all the sum of all the factors other than itself adds to the number itself. This makes the sum of its reciprocals 2.

Answer 2

The sum of the reciprocals of the positive integer factors of 28 is 56.

Step-by-step explanation:

The positive integer factors of 28 are 1, 2, 4, 7, 14, and 28. To find the sum of their reciprocals, we simply add up the reciprocals of each factor. The reciprocal of a number is found by taking 1 divided by the number.

So the sum would be:

1/1 + 1/2 + 1/4 + 1/7 + 1/14 + 1/28 = 1 + 1/2 + 1/4 + 1/7 + 1/14 + 1/28

To simplify this further, we need to find a common denominator. The least common multiple of the denominators is 28, so we can rewrite each fraction with a denominator of 28:

28/28 + 14/28 + 7/28 + 4/28 + 2/28 + 1/28 = 28/28 + 14/28 + 7/28 + 4/28 + 2/28 + 1/28

Now we can add the fractions:

28 + 14 + 7 + 4 + 2 + 1 = 56

Therefore, the sum of the reciprocals of the positive integer factors of 28 is 56.