Q: What are the factor combinations of the number 420,220,045?

 A:
Positive:   1 x 4202200455 x 840440097 x 6003143535 x 12006287281 x 14954451405 x 2990891967 x 2136359835 x 42727
Negative: -1 x -420220045-5 x -84044009-7 x -60031435-35 x -12006287-281 x -1495445-1405 x -299089-1967 x -213635-9835 x -42727


How do I find the factor combinations of the number 420,220,045?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 420,220,045, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 420,220,045
-1 -420,220,045

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 420,220,045.

Example:
1 x 420,220,045 = 420,220,045
and
-1 x -420,220,045 = 420,220,045
Notice both answers equal 420,220,045

With that explanation out of the way, let's continue. Next, we take the number 420,220,045 and divide it by 2:

420,220,045 ÷ 2 = 210,110,022.5

If the quotient is a whole number, then 2 and 210,110,022.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 420,220,045
-1 -420,220,045

Now, we try dividing 420,220,045 by 3:

420,220,045 ÷ 3 = 140,073,348.3333

If the quotient is a whole number, then 3 and 140,073,348.3333 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 420,220,045
-1 -420,220,045

Let's try dividing by 4:

420,220,045 ÷ 4 = 105,055,011.25

If the quotient is a whole number, then 4 and 105,055,011.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 420,220,045
-1 420,220,045
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

157352811,4051,9679,83542,727213,635299,0891,495,44512,006,28760,031,43584,044,009420,220,045
-1-5-7-35-281-1,405-1,967-9,835-42,727-213,635-299,089-1,495,445-12,006,287-60,031,435-84,044,009-420,220,045

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