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Which of the following mathematical statements is not true?

  • A.The number of factors of a given number is finite
  • B.Every factor of a given number is less than or equal to the given number
  • C.Every factor of a given number is always greater than the given number
  • D.Every multiple of a given number is greater than or equal to that number

Answer: C

The statement that is not true is Every factor of a given number is always greater than the given number.

A factor divides the number exactly, so for natural numbers it can never exceed the number; the largest factor is the number itself. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12.

The other statements are true. Every number has finitely many factors (A). Every factor is less than or equal to the number (B). Every multiple, such as 12, 24, 36 for 12, is greater than or equal to the number (D).

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