Remember that for any integer $n$ , the integers $1 \text{and} n$ are both divisors (or factors) of $n$ . First, we will prove that n is a square, and then we will compute the factors of the n².

In this case, the integer n has exactly two different divisors greater than 1. It's impossible that $n=1$ , since 1 doesn't have positive factors greater than 1. Then $n>1$ , therefore $n$ itself is one of the required divisors. Denote by $a$ the other divisor greater than 1, and note that to satisfy the condition on the divisors, $a$ .

Because a divides n, there exists some integer $k$ such that $n=ak$ . We must have that $k>1$ , if not, then $k\leq 1$ , which implies that $ak=n\leq a$ , which contradicts the part above.

Now, $k>1$ and, by definition of divisibility, k divides n. Then k must be equal either to n or a, since we can't have three different divisors of this kind. If $k=n$ then $n=an$ and by cancellation, $1=a$ which is a contradiction. Therefore $k=a$ and $n=a^2$ .

We have that $n=(a^2)^2=a^4$ . We can write n as $n=a^3a=a^2a^2=a^4 \cdot 1$ . From the first equation, a divides n and a³ divides n. From the second equation, a² divides, and from the last one, 1 divides n and a⁴=n divides n. Thus n has exactly 5 positive factors.

4 0

4 years ago

So is 80 kilometers bigger than 1000 meters

Sergeu [11.5K]

80 kilometers is equal to 80,000 meters. This is greater than 1000 meters.

3 0

3 years ago

Read 2 more answers

Use the number line to add the fraction. Pls helppp

PtichkaEL [24]

Answer: 1/6

-1/2 also equals -3/6

2/3 also equals 4/6

Using the number line, start at -1/2. Then, since the distance from one dash to the next on the line equals 1/6, you will move 4 spaces to the right. That should give you 1/6.

7 0

4 years ago