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Is one a multiple of every number?

Understand the Problem

The question is asking whether the number one can be considered a multiple of every other number. This relates to the definitions of multiples and divisibility in mathematics.

Answer

No, the number one is not a multiple of every other number.
Answer for screen readers

No, the number one is not a multiple of every other number.

Steps to Solve

  1. Definition of a multiple

A number $A$ is considered a multiple of another number $B$ if there exists an integer $n$ such that $A = n \cdot B$.

  1. Checking if 1 is a multiple of another number

We need to check if there is an integer $n$ such that $1 = n \cdot B$ for any number $B$.

  1. Analyzing the equation

Rearranging the equation, we have $n = \frac{1}{B}$.

  1. Examining different values of $B$

For any integer value of $B$ where $B \neq 0$, if $B$ is greater than 1, then $\frac{1}{B}$ will not be an integer. Therefore, $n$ cannot be an integer for those values.

  1. Special case: when B = 1

If $B = 1$, then $n$ becomes $\frac{1}{1} = 1$, which is an integer.

  1. Conclusion

Since $1$ does not equal $n \cdot B$ for all $B$, we conclude that $1$ is only a multiple of itself and not of other integers.

No, the number one is not a multiple of every other number.

More Information

The number one can only be considered a multiple of itself because it doesn't satisfy the definition of multiples with any other integer. This subtle understanding helps clarify how multiples work in relation to divisibility.

Tips

  • Thinking that 1 is a multiple of all integers; it is not because it lacks integer multiples with numbers greater than itself.
  • Confusing the concept of factors with multiples; a factor can divide a number evenly, while a multiple is derived by multiplication.
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