Question

consider the following statement. for all integers a, b, and c, if a is a factor of c and b is a factor of c then ab is a factor of c. is the statement true or false? find values of a, b, and c that can be used to answer this question. enter them here. (a, b, c)_________.

Answer 1

The statement is false. As an example, a=2, b=3, and c=6 shows that while a and b are factors of c, the product ab is equal to c but not a factor of c.

Step-by-step explanation:

The statement that for all integers a, b, and c, if a is a factor of c and b is a factor of c then ab is a factor of c is false. To illustrate this, consider a = 2, b = 3, and c = 6. Both 2 and 3 are factors of 6, but their product, 6, is not a factor of 6. It is important to understand that factors of a number must divide that number without leaving a remainder, and the product of two factors of a number will not always satisfy that condition unless the number is a multiple of their product.