2.) Prime Factorization
This strategy is taught in school, but it’s often underused in real-world mental math.
Any non-prime number can be expressed as a product of prime “building blocks.”
For example:
- 124 = 2 × 2 × 31
- 125 = 5 × 5 × 5
- 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 26 × 3
When you multiply by a number like 192, you’re really multiplying by six 2’s and one 3.
So instead of thinking:
“multiply by 192”
You can think:
“multiply by 2 six times, and by 3 once.”
This is powerful because multiplication is associative and commutative. You can reorder these factors however you want.
That means you can:
- group operations into easier steps
- simplify along the way
- choose the most convenient order
Example:
25 × 192
Rewrite:
25 × (26 × 3)
Now reorder:
(25 × 4) × (24 × 3)
Since:
- 25 × 4 = 100
You get:
100 × 16 × 3 = 1600 × 3 = 4800
Another example:
36 × 125
Rewrite:
36 × (5 × 5 × 5)
Reorder to make a friendly number:
(36 × 5) × 25
- 36 × 5 = 180
- 180 × 25 = 4500
By grouping strategically, the calculation becomes much easier than multiplying directly.
Prime factorization lets you:
- break numbers into flexible pieces
- recombine them into easier calculations
- reduce mental load by creating “friendly” intermediate values
It’s especially useful for:
- multiplication
- division
- simplifying fractions
- recognizing hidden structure in numbers
Over time, this way of thinking changes how you see numbers.
Instead of viewing numbers as fixed values, you begin to see them as combinations of smaller, reusable parts, almost like they’re built from a common set of units.
The more you think in prime factors, the more freedom you gain.
You’re no longer stuck with the number you’re given, but free to reshape it into something easier to work with.