5.) Expanding the Multiplication Table (Start with Primes)
There’s a reason multiplication tables are taught early and emphasized so heavily. Memorizing these facts gives you a kind of arithmetic “Swiss army knife,” allowing your brain to offload basic computations into long-term memory.
But if you want to go beyond the standard table, the most efficient approach isn’t to memorize everything in order.
A better strategy is to focus on prime numbers.
Prime numbers are the building blocks of all other numbers.
So instead of memorizing:
- multiples of 13
- then 14
- then 15
- then 16
you can skip ahead and focus on:
- 13
- 17
- 19
If you know your prime multiples well, you can reconstruct many composite ones:
- 14 = 2 × 7
- 15 = 3 × 5
- 16 = 2⁴
So:
- 14 × 6 → (2 × 7) × 6 → 7 × 12 = 84
- 15 × 8 → (3 × 5) × 8 → 3 × 40 = 120
Another example:
18 × 7
Instead of memorizing 18 × 7 directly, break it into primes:
18 = 2 × 3 × 3
Now rearrange:
(2 × 3 × 3) × 7 → 3 × (3 × 14) → 3 × 42 = 126
This kind of factor-based thinking lets you build answers from pieces you already know.
You’re not memorizing more—you’re reusing what you already know.
If you only have time to expand your mental math toolkit—say, during a long car ride or flight—focusing on primes gives you the highest return on effort.
Each new prime you learn:
- unlocks many composite numbers
- strengthens factor-based thinking
- connects directly to strategies like decomposition and prime factorization
This approach shifts your thinking from memorizing isolated facts to building a connected system of relationships.
Over time, multiplication stops feeling like recall—and starts feeling like navigation.
Primes don’t just add more facts to your memory—they make the entire system more flexible.