Special Integers

Certain integers have special properties and factorizations that are frequently used in problems. Memorizing these can turn a complex multiplication into a simple one.

• 999 = 27 × 37. (Used for problems with multiples of 37 or 27, like 333, 111, etc.)
• 1001 = 7 × 11 × 13. (This is useful for divisibility and multiplication involving these primes). Numbers like 77, 143, etc., are derived from this.
• 10101 = 3 × 7 × 13 × 37. (Used for divisibility and multiplication involving these primes).

For example, to solve $1443 \times 56$, you can recognize that $1443 = \frac{10101}{7}$. So the problem becomes $\frac{10101}{7} \times 56 = 10101 \times 8 = 80808$.