Remainders

It is given a set of numbers { 117; 136; 363; 419; 575; 651 }. Divide these numbers by number 58 and determine a set of remainders. As a result, write the sum of these remainders.

Correct answer:

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Dr. Math

To solve this problem, we will divide each number in the set by 58 and determine the remainder for each division. Then, we will sum all the remainders.

Given Set of Numbers:

{ 117, 136, 363, 419, 575, 651 }

Step 1: Divide Each Number by 58 and Find the Remainder

1. 117 ÷ 58:
- 58 × 2 = 116 .
- Remainder = 117 - 116 = 1 .

2. 136 ÷ 58:
- 58 × 2 = 116 .
- Remainder = 136 - 116 = 20 .

3. 363 ÷ 58:
- 58 × 6 = 348 .
- Remainder = 363 - 348 = 15 .

4. 419 ÷ 58:
- 58 × 7 = 406 .
- Remainder = 419 - 406 = 13 .

5. 575 ÷ 58:
- 58 × 9 = 522 .
- Remainder = 575 - 522 = 53 .

6. 651 ÷ 58:
- 58 × 11 = 638 .
- Remainder = 651 - 638 = 13 .

Step 2: Write the Set of Remainders
The remainders are:

{ 1, 20, 15, 13, 53, 13 }.

Step 3: Sum the Remainders
Add all the remainders together:

1 + 20 + 15 + 13 + 53 + 13 = 115.

Final Answer:
The sum of the remainders is: