Given $P = 23,467,894,057,475 \times 753 + 1984$ Find the exact values of the quotient and the remainder when $P$ is divided by $753$ . IMPORTANT: you have to solve this problem without performing multiplication, addition, and division.

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Algebra 2

Complex conjugate theorem

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Q. Given

P = 23,467,894,057,475 \times 753 + 1984

Find the exact values of the quotient and the remainder when

P

is divided by

753

. IMPORTANT: you have to solve this problem without performing multiplication, addition, and division.

Define P Calculation: Since P is defined as $P = 23,467,894,057,475 \times 753 + 1984$ , we can see that P is the result of multiplying a number by $753$ and then adding $1984$ . When we divide P by $753$ , the quotient will be the number that was multiplied by $753$ , and the remainder will be the amount that was added after the multiplication, which is $1984$ , as long as $1984$ is less than $753$ .
Check Remainder Condition: We need to check if the remainder $1984$ is less than the divisor $753$ . If it is, then $1984$ is indeed the remainder. If it is not, we would have to adjust our answer.
Calculate Correct Remainder: Comparing $1984$ and $753$ , we see that $1984$ is greater than $753$ . This means that $1984$ cannot be the remainder when dividing by $753$ , because the remainder must be less than the divisor. We need to divide $1984$ by $753$ to find the correct remainder.
Find Quotient and Remainder: Dividing $1984$ by $753$ , we get $2$ as the quotient and a remainder. To find the remainder, we calculate $1984 - 2 \times 753$ .
Find Quotient and Remainder: Dividing $1984$ by $753$ , we get $2$ as the quotient and a remainder. To find the remainder, we calculate $1984 - 2 \times 753$ .The calculation gives us $1984 - 2 \times 753 = 1984 - 1506 = 478$ . So, the remainder when $1984$ is divided by $753$ is $478$ .
Find Quotient and Remainder: Dividing $1984$ by $753$ , we get $2$ as the quotient and a remainder. To find the remainder, we calculate $1984 - 2 \times 753$ .The calculation gives us $1984 - 2 \times 753 = 1984 - 1506 = 478$ . So, the remainder when $1984$ is divided by $753$ is $478$ .Now we have the correct remainder, which is $478$ . The quotient when P is divided by $753$ is the original number that was multiplied by $753$ , which is $23,467,894,057,475$ , and the remainder is $478$ .