The DNA of Numbers
In mathematics, a prime number is an integer greater than 1 that can only be divided evenly by 1 and itself (e.g., 2, 3, 5, 7, 11).
Prime Factorization is the process of breaking down a composite number into a set of prime numbers that, when multiplied together, equal the original number. You can think of prime factors as the fundamental building blocks—or the "DNA"—of all other numbers.
The Fundamental Theorem of Arithmetic
This famous theorem states that every integer greater than 1 is either a prime number itself, or it can be represented as a product of prime numbers. Furthermore, this specific combination of prime numbers is 100% unique to that integer, much like a fingerprint.
Divisibility Rules Cheat Sheet
When doing a factor tree by hand, use these quick mental math tricks to figure out which prime number to divide by first:
Divisible by 2
If the number ends in an even digit (0, 2, 4, 6, 8).
Divisible by 3
If the sum of all its digits is divisible by 3 (e.g., 27: 2+7=9, 9÷3=3).
Divisible by 5
If the number ends in a 0 or a 5.
Divisible by 7, 11, 13...
No easy trick! If 2, 3, and 5 don't work, you must manually test division by the next consecutive prime numbers.