Changes

:<math>(3 + 1) * (1 + 1) = 8</math>

:<math>(3 + 1) * (1 + 1) = 8</math>

and they are 1, 2, 3, 4, 6, 8, 12, and 24.

and they are 1, 2, 3, 4, 6, 8, 12, and 24. To show this in general, suppose that n = 2^a 3^b 5^c.  Then the factors of n are exactly the numbers 2^j 3^k 5^l, where j is between 0 and a, k is between 0 and b, and l is between 0 and c.  So the number of factors is just the number of choices for j, times the number of choices for k, times the number of choices for l, which is (a+1)(b+1)(c+1).

==Other uses==

==Other uses==

The word factor also appears in other contexts, such as algebra. A [[polynomial]], such as x³+3x²+2x, may be decomposed into a product of linear terms (terms of the form (ax+b) where a and b are real numbers, and a is nonzero); for example, x³+3x²+2x=x(x+1)(x+2). These linear terms are called the factors of the polynomial, and the process of determining the factors is called [[factorization]].

The word factor also appears in other contexts, such as algebra. A [[polynomial]], such as x³+3x²+2x, may be decomposed into a product of linear terms (terms of the form (ax+b) where a and b are real numbers, and a is nonzero); for example, x³+3x²+2x=x(x+1)(x+2). These linear terms are called the factors of the polynomial, and the process of determining the factors is called [[factorization]].

[[Category:Mathematics]]

[[Category:Arithmetic]]