Q: What are the factor combinations of the number 401,000,016?

 A:
Positive:   1 x 4010000162 x 2005000083 x 1336666724 x 1002500046 x 668333368 x 5012500212 x 3341666816 x 2506250119 x 2110526424 x 1670833438 x 1055263248 x 835416757 x 703508876 x 5276316114 x 3517544152 x 2638158228 x 1758772304 x 1319079456 x 879386912 x 439693
Negative: -1 x -401000016-2 x -200500008-3 x -133666672-4 x -100250004-6 x -66833336-8 x -50125002-12 x -33416668-16 x -25062501-19 x -21105264-24 x -16708334-38 x -10552632-48 x -8354167-57 x -7035088-76 x -5276316-114 x -3517544-152 x -2638158-228 x -1758772-304 x -1319079-456 x -879386-912 x -439693


How do I find the factor combinations of the number 401,000,016?

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 401,000,016, 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.

1 401,000,016
-1 -401,000,016

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 401,000,016.

Example:
1 x 401,000,016 = 401,000,016
and
-1 x -401,000,016 = 401,000,016
Notice both answers equal 401,000,016

With that explanation out of the way, let's continue. Next, we take the number 401,000,016 and divide it by 2:

401,000,016 ÷ 2 = 200,500,008

If the quotient is a whole number, then 2 and 200,500,008 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

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

1 2 200,500,008 401,000,016
-1 -2 -200,500,008 -401,000,016

Now, we try dividing 401,000,016 by 3:

401,000,016 ÷ 3 = 133,666,672

If the quotient is a whole number, then 3 and 133,666,672 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

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

1 2 3 133,666,672 200,500,008 401,000,016
-1 -2 -3 -133,666,672 -200,500,008 -401,000,016

Let's try dividing by 4:

401,000,016 ÷ 4 = 100,250,004

If the quotient is a whole number, then 4 and 100,250,004 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

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

1 2 3 4 100,250,004 133,666,672 200,500,008 401,000,016
-1 -2 -3 -4 -100,250,004 -133,666,672 -200,500,008 401,000,016
Keep dividing by the next highest number until you cannot divide anymore.

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

1234681216192438485776114152228304456912439,693879,3861,319,0791,758,7722,638,1583,517,5445,276,3167,035,0888,354,16710,552,63216,708,33421,105,26425,062,50133,416,66850,125,00266,833,336100,250,004133,666,672200,500,008401,000,016
-1-2-3-4-6-8-12-16-19-24-38-48-57-76-114-152-228-304-456-912-439,693-879,386-1,319,079-1,758,772-2,638,158-3,517,544-5,276,316-7,035,088-8,354,167-10,552,632-16,708,334-21,105,264-25,062,501-33,416,668-50,125,002-66,833,336-100,250,004-133,666,672-200,500,008-401,000,016

More Examples

Here are some more numbers to try:

401,000,014401,000,015401,000,017401,000,018
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