Which expression has both 8 and n as factors?

Audrey Hall

Audrey Hall

Answered question

2023-04-01

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

Answer & Explanation

8len2dstjvj

8len2dstjvj

Beginner2023-04-02Added 3 answers

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·(2)=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

nick1337

Expert2023-06-13Added 777 answers

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 23.
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 = 23×n = 8n
Therefore, the expression that has both 8 and n as factors can be written as 8n.
Don Sumner

Don Sumner

Skilled2023-06-13Added 184 answers

The prime factorization of 8 is 23, 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 p1a1·p2a2··pkak, where p1,p2,,pk are distinct prime numbers and a1,a2,,ak 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 23·p1a1·p2a2··pkak.
Vasquez

Vasquez

Expert2023-06-13Added 669 answers

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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