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
- Definition of a multiple
A number $A$ is considered a multiple of another number $B$ if there exists an integer $n$ such that $A = n \cdot B$.
- 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 $B$.
- Analyzing the equation
Rearranging the equation, we have $n = \frac{1}{B}$.
- 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.
- Special case: when B = 1
If $B = 1$, then $n$ becomes $\frac{1}{1} = 1$, which is an integer.
- 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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