Divisor 16807
- Prime Number:
- No, but it is a power of a prime: 75
Test for Divisibility by 16807
To determine if any number is divisible by 16807, apply this test:
- If your number ("X") has 8 digits or more, separate the last (smallest) 7 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 8 digits, L = 0 and therefore R = X.
- Multiply L by 165 and subtract this from R.
- Take that result and cross off its final digit (units). Take this new number and subtract 5042 times the digit you just crossed off. Call this final result "Y".
- Y will be much smaller than X, but we have preserved divisibility by 16807. That is, your original number is divisible by 16807 if (and only if) Y is. Now that it's much smaller, with basic knowledge of your 16807-times tables, it should be easy to visually see if Y is divisible by 16807. If the Y is still much larger than 16807, the above process can be repeated until it does reduce to within small multiples of 16807.
Easy!