Factors are the divided parts of a larger number or expression. Dividing an expression by one of its factors should simplify the expression (or number). Its important to note that factors generally are integers and do NOT contain fractions or decimals.
Factoring is a process used to obtain the factors of a number or expression. There are multiple methods used to factor and it generally takes practice to find the method or methods that work best.
Observations on numeric factors:
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- ZERO is never a factor and cannot itself be factored.
- Any number and ‘1‘ are ALWAYS two of the factors.
- Prime numbers CANNOT be factored.
- 1, 3, 5, 7, 11, 17, 19, 23, 29, 31, 37, and so on.
- Even numbers can ALWAYS be divided by ‘2‘.
- Negative numbers are generally not considered as factors.
- Factoring often continues until all factors are prime numbers.
- The result factors are often called the PRIME FACTORS.
- Some factors may be repeated (factoring 8 gives 2, 2, and 2)
- 2 x 2 = 4 and 2 x 4 = 8.
Examples:
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- 15 has factors of 1, 3, 5, and 15.
- 24 has factors of 1, 2, 3, 4, 6, 8, 12
- Its prime factors are: 1, 2, and 3.
- 2 x 2 = 4 –> 2 x 4 = 8 –> 8 x 3 = 24.
- 37 has only the factors of 1 and 37 (It is prime).
- 32 has factors of 1, 2, 4, 8, 16, and of course 32.
- Its prime factors are 1 and 2.
- 2 x 2 = 4 –> 4 x 2 = 8 –> 8 x 2 = 16, and 16 x 2 = 32