Remainders
It is given a set of numbers { 200; 261; 331; 345; 487; 554 }. Divide these numbers by number 80 and determine a set of remainders. As a result, write the sum of these remainders.
Final 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.
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 .
The remainders are:
Add all the remainders together:
The sum of the remainders is:
Given Set of Numbers:
{ 117, 136, 363, 419, 575, 651 }
Step 1:
Divide Each Number by 58 and Find the Remainder1. 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 RemaindersThe remainders are:
{ 1, 20, 15, 13, 53, 13 }.
Step 3:
Sum the RemaindersAdd all the remainders together:
1 + 20 + 15 + 13 + 53 + 13 = 115.
Final Answer:
The sum of the remainders is:
115
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