I'm working on an elementary number theory book for fun and I have come across the following problem:
Find the prime-power decomposition of 999,999,999,999 (Note that $101 \mid 1000001$.).
Other than just mindlessly guessing primes that divide it, how should I go about finding the solution? I am curious as to how this hint about 101 dividing 1000001 helps. There is also a factor table for integers less than 10,000 in the back of the book, so really the objective is to get 999,999,999,999 down to a product of numbers with less than 5 digits, then I can just use the table.