About Factoring
In mathematics, factoring (or factorization) is the process of breaking down a number into smaller numbers that, when multiplied together, give you the original number. These smaller numbers are called factors.
Key Concepts
- Factor: A number that divides another number evenly, with no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Prime Number: A number greater than 1 that has only two factors: 1 and itself. Examples include 2, 3, 5, 7, 11.
- Composite Number: A number greater than 1 that is not prime. It has more than two factors.
- Prime Factorization: The process of finding the prime numbers that multiply together to make the original number. For example, the prime factorization of 12 is 2 × 2 × 3.
How to Find Factors
To find all the factors of a number, you can test each integer from 1 up to the square root of the number. If a number divides evenly, then both that number and the result of the division are factors. For example, to find the factors of 100:
- Start with 1. 100 / 1 = 100. So, 1 and 100 are factors.
- Try 2. 100 / 2 = 50. So, 2 and 50 are factors.
- 3 does not divide evenly.
- Try 4. 100 / 4 = 25. So, 4 and 25 are factors.
- And so on, up to 10 (the square root of 100).