let num = +prompt("give us a number")
while (num % 7 != 0) {

    if (num > 0){
        document.write("positive ")
        if(num % 7 == 0) {
        break;
    } else {
        num = +prompt("give us a number") 
    } 
    } else if (num < 0) {
        document.write("negative ")
        if(num % 7 == 0) {
        break;
    } else {
        num = +prompt("give us a number") 
    } 
    } else if (num === 0) {
        document.write("zero ")
        if(num % 7 == 0) {
        break;
    } else {
        num = +prompt("give us a number") 
    } 
    }
}

Either bring out the else if (num == 0) part before while loop

since 0 % 7 == 0 is true it should satisfy the excersise even if it's not in the loop.

if (num == 0) {
  // do stuff
}
while (/* condition */) {
  // do other stuff
}

Or add num == 0 constraint in while condition.

while (num == 0 || num % 7 != 0) {
  // do stuff
}

The former will not get into the loop, the latter will cause the loop to exit on num == 0 because both implies that it's a correct modulo division.

You can do both if you want to optimize memory usage (obviously it wouldn't be a problem in this scale).

This may be one possible way to achieve the desired objective.

Code Sample This sample uses alert to pop-up the result, instead of document.write.

let num = 1;
while (!num || num % 7) {
  num = +prompt('enter a number');
  if (num && num % 7) {
    alert(
      `${num} is ${num > 0
        ? 'positive'
        : 'negative'
      }`
    );
  } else if (!num) alert('num is zero');
};

Explanation

• Set an initial value of num to 1
• Set a while loop which will execute as long as num is not 0 (falsy, technically) and num % 7 is not 0.
• Get the user-input using prompt into the variable num
• If num is truthy (ie, non-zero) and num % 7 is truthy (ie, non-zero), pop an alert whether num is positive (if > 0) or negative (otherwise). This is achieved by using ` backtick symbol / template literal and ?: ternary-operator.
• Else, if num is zero, then pop-up corresponding alert

Code Snippet

let num = 1;
while (!num || num % 7) {
  num = +prompt('enter a number');
  if (num && num % 7) {
    alert(
      `${num} is ${num > 0
        ? 'positive'
        : 'negative'
      }`
    );
  } else if (!num) alert('num is zero');
};