Question

What is the product of all positive divisors of $10$?

Answer 1

positive divisors of 10: 1,2,5,10

`1\cdot2\cdot5\cdot10=100`

Answer 2

The product of all positive divisors of $10 is 100

Explanation:

Given

$10

Required

Product of all positive divisors.

Before we can get the product of all positive divisors of $10, we need to get the divisors.

The most basic method for calculating divisors is exhaustive trial division.

This method might not be efficient for large numbers but since 10 is not large, we'll make use of this trial division method.

To find the positive divisors for an integer n,

we divide n by integers 1, 2, 3, ... ,n/2, n

So, for $10, we'll try the following numbers

1,2,3,4,5,10

1:
`(10)/(1) = 10` ---- is a divisor

2:
`(10)/(2) = 5` ---- is a divisor

3:
`(10)/(3) = 3.33` ---- is not a divisor

4:
`(10)/(4) = 2.5` ---- is not a divisor

5:
`(10)/(5) = 2` ---- is a divisor

10:
`(10)/(10) = 1` ---- is a divisor

Now, that we have the divisor of 10 to be 1,2,5,10.

The next step is to multi[ply these numbers

1 * 2 * 5 * 10 = 100

The product of all positive divisors of $10 is 100