# what are the factors of 120

2*60
2*2*30
2*2*2*15
2*2*2*3*5
can you take it any further?

123456789

## To find the factors of a number like 120, you start by dividing it by numbers starting from 1 and going up to the square root of the number.

For example, let's try dividing 120 by the numbers from 1 to 10:

- 120 ÷ 1 = 120
- 120 ÷ 2 = 60
- 120 ÷ 3 = 40
- 120 ÷ 4 = 30
- 120 ÷ 5 = 24
- 120 ÷ 6 = 20
- 120 ÷ 7 = 17.14 (not a whole number)
- 120 ÷ 8 = 15
- 120 ÷ 9 = 13.33 (not a whole number)
- 120 ÷ 10 = 12

Now, we can see that the factors of 120 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

These numbers can be further factored. For example, let's pick 2 and factor it:

- 2 ÷ 1 = 2
- 2 ÷ 2 = 1

So, the prime factors of 2 are 1 and 2.

Using the same process, we can further factor the other numbers in the list of factors of 120.

For example, let's take 60:
- 60 ÷ 1 = 60
- 60 ÷ 2 = 30
- 60 ÷ 3 = 20
- 60 ÷ 4 = 15
- 60 ÷ 5 = 12
- 60 ÷ 6 = 10
- 60 ÷ 10 = 6
- 60 ÷ 12 = 5

So, the prime factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

We can continue this process for each factor of 120 to find their prime factors.

Now, moving on to the number 123456789, this is a large number that we can break down using the approach of finding factors I described above.

Let's try dividing 123456789 by the numbers from 1 to 10:

- 123456789 ÷ 1 = 123456789
- 123456789 ÷ 2 = 61728394.5 (not a whole number)

It seems that 2 is not a factor of 123456789, so we can stop here. The factors of 123456789 are then 1 and 123456789.