Learn prime factorization and find greatest common factor and least common multiple. Math 10-C Alberta.
Lesson 4.1 of Factors and Roots in Math 10C — Alberta curriculum lessons.
Definition — Prime Number. A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself.
It cannot be divided evenly by any other whole number.
The first several primes:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Definition — Composite Number. A composite number is a whole number greater than 1 that has more than two factors — meaning it can be broken down further.
Every composite number can be written as a product of primes.
Special Cases — 1 and 2. The number 1 is neither prime nor composite — it has only one factor (itself).
The number 2 is the only even prime number. Every other even number is divisible by 2, so it has at least three factors and is composite.
Finding Factors. The factors of a number are all the whole numbers that divide into it evenly.
To find them, check every number from 1 up to the square root — each divisor you find gives you a factor pair.
Example — Factors of 36. Step 1 — List the factor pairs:
1 × 36
2 × 18
3 × 12
4 × 9
6 × 6
Step 2 — Collect all unique values:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
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