Which statement about factors is correct?

Which statement about factors is correct?

• A. Factors are always even
• B. Factors can only be whole numbers
• C. Every number has exactly two factors
• D. A factor of a number cannot exceed the number

Answer: (D)

The statement that a factor of a number cannot exceed the number is correct because by definition, a factor is a number that divides another number without leaving a remainder. For instance, if you consider the number 12, its factors include 1, 2, 3, 4, 6, and 12. None of these factors are greater than 12 itself. In general, for any integer \( n \), a factor \( f \) must satisfy the condition that \( f \leq n \). This rule holds true for all integers, ensuring that a factor cannot be larger than the number it divides, thus supporting the validity of the statement.

The statement that a factor of a number cannot exceed the number is correct because by definition, a factor is a number that divides another number without leaving a remainder. For instance, if you consider the number 12, its factors include 1, 2, 3, 4, 6, and 12. None of these factors are greater than 12 itself. In general, for any integer ( n ), a factor ( f ) must satisfy the condition that ( f \leq n ). This rule holds true for all integers, ensuring that a factor cannot be larger than the number it divides, thus supporting the validity of the statement.