Question #21161

Let n = akak-1ak-2. . .a1a0 be an integer and t = a0 - a1 + a2 - + (-1)k ak. It

is known that n is divisible by 11 if and only if t is divisible by 11. For

example, suppose that n = 8784204. Then, t = 4 - 0 + 2 - 4 + 8 - 7 + 8 =

11. Because 11 is divisible by 11, it follows that 8784204 is divisible by 11.

If n ¼ 54063297, then t = 7 - 9 + 2 - 3 + 6 - 0 + 4 - 5 = 2. Because 2 is not divisible by 11, 54063297 is not divisible by 11.Write a program that

prompts the user to enter a positive integer and then uses this criterion to

determine whether the number is divisible by 11.

is known that n is divisible by 11 if and only if t is divisible by 11. For

example, suppose that n = 8784204. Then, t = 4 - 0 + 2 - 4 + 8 - 7 + 8 =

11. Because 11 is divisible by 11, it follows that 8784204 is divisible by 11.

If n ¼ 54063297, then t = 7 - 9 + 2 - 3 + 6 - 0 + 4 - 5 = 2. Because 2 is not divisible by 11, 54063297 is not divisible by 11.Write a program that

prompts the user to enter a positive integer and then uses this criterion to

determine whether the number is divisible by 11.

Expert's answer

#include <iostream>

#include <conio.h>

using namespace std;

void main()

{

long long number;

cout << "Enter a positive integer: ";

cin >> number;

char digit;

char sign = 1;

int sum = 0;

while (number > 0)

{

digit = number % 10;

number /= 10;

sum += sign * digit;

sign *= -1;

}

if (sum % 11 == 0)

cout << number << " is divisible by 11." << endl;

else

cout << number << " is not divisible by 11." << endl;

getch();

}

#include <conio.h>

using namespace std;

void main()

{

long long number;

cout << "Enter a positive integer: ";

cin >> number;

char digit;

char sign = 1;

int sum = 0;

while (number > 0)

{

digit = number % 10;

number /= 10;

sum += sign * digit;

sign *= -1;

}

if (sum % 11 == 0)

cout << number << " is divisible by 11." << endl;

else

cout << number << " is not divisible by 11." << endl;

getch();

}

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