Audrey Hall

2023-04-01

Which expression has both 8 and n as factors???

8len2dstjvj

The expression that has both 8 and $n$ as factors is given by $E=8n$.
In this expression, the number 8 and the variable $n$ are multiplied together. This means that any value of $n$ multiplied by 8 will satisfy the expression.
For example, if we let $n=3$, then $E=8·3=24$, which shows that both 8 and 3 are factors of 24.
Similarly, if we let $n=-2$, then $E=8·\left(-2\right)=-16$, which again demonstrates that both 8 and -2 are factors of -16.
Thus, the expression $E=8n$ represents the relationship where both 8 and $n$ are factors.

nick1337

Result:
The expression that has both 8 and $n$ as factors is $8n$.
Solution:
An expression that has 8 as a factor can be written as $8×k$, where $k$ is an integer. Similarly, an expression that has $n$ as a factor can be written as $n×m$, where $m$ is an integer.
To find the expression that satisfies both conditions, we need to find a common multiple of 8 and $n$. In other words, we are looking for the least common multiple (LCM) of 8 and $n$.
To calculate the LCM, we need to find the prime factorization of 8 and $n$. Let's start with 8:
The prime factorization of 8 is $2×2×2$ or ${2}^{3}$.
For $n$, we do not have any specific information, so we will keep it as $n$ in its prime factorization.
Now, let's calculate the LCM by taking the highest power of each prime factor that appears in either 8 or $n$:
LCM = ${2}^{3}×n$ = $8n$
Therefore, the expression that has both 8 and $n$ as factors can be written as $8n$.

Don Sumner

The prime factorization of 8 is ${2}^{3}$, which means it can be written as $2·2·2$.
The prime factorization of $n$ is dependent on the specific value of $n$ and may vary. Let's assume that the prime factorization of $n$ is ${p}_{1}^{{a}_{1}}·{p}_{2}^{{a}_{2}}·\dots ·{p}_{k}^{{a}_{k}}$, where ${p}_{1},{p}_{2},\dots ,{p}_{k}$ are distinct prime numbers and ${a}_{1},{a}_{2},\dots ,{a}_{k}$ are their respective exponents.
To have both 8 and $n$ as factors in an expression, we need at least three 2's from the prime factorization of 8 and all the prime factors from the prime factorization of $n$. Thus, the expression can be written as ${2}^{3}·{p}_{1}^{{a}_{1}}·{p}_{2}^{{a}_{2}}·\dots ·{p}_{k}^{{a}_{k}}$.

Vasquez

To solve the expression ''Which expression has both 8 and n as factors?'', we can represent it algebraically as:
$8·n$
The expression $8·n$ has both 8 and n as factors.

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