Divisor 991

Prime Number:
Yes!

Test for Divisibility by 991

To determine if any number is divisible by 991, apply this test:

  1. If your number ("X") has 4 digits or more, separate the last (smallest) 3 digits from the rest. This makes two smaller numbers, call them Left and Right (note: don't add in trailing zeros to L). If there are fewer than 4 digits, L = 0 and therefore R = X.
  2. Multiply L by 9 and add to R.
  3. Take that result and cross off its final digit (units). Take this new number and subtract 99 times the digit you just crossed off. Call this final result "Y".
  4. Y will be much smaller than X, but we have preserved divisibility by 991. That is, your original number is divisible by 991 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 991-times tables, it should be easy to visually see if Y is divisible by 991. If the Y is still much larger than 991, the above process can be repeated until it does reduce to within small multiples of 991.

Easy!