Q: What are the factor combinations of the number 102,001,031?

 A:
Positive:   1 x 10200103111 x 927282143 x 237211789 x 1146079473 x 215647979 x 1041892423 x 420973827 x 26653
Negative: -1 x -102001031-11 x -9272821-43 x -2372117-89 x -1146079-473 x -215647-979 x -104189-2423 x -42097-3827 x -26653


How do I find the factor combinations of the number 102,001,031?

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 102,001,031, 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.

1 102,001,031
-1 -102,001,031

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 102,001,031.

Example:
1 x 102,001,031 = 102,001,031
and
-1 x -102,001,031 = 102,001,031
Notice both answers equal 102,001,031

With that explanation out of the way, let's continue. Next, we take the number 102,001,031 and divide it by 2:

102,001,031 ÷ 2 = 51,000,515.5

If the quotient is a whole number, then 2 and 51,000,515.5 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:

1 102,001,031
-1 -102,001,031

Now, we try dividing 102,001,031 by 3:

102,001,031 ÷ 3 = 34,000,343.6667

If the quotient is a whole number, then 3 and 34,000,343.6667 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:

1 102,001,031
-1 -102,001,031

Let's try dividing by 4:

102,001,031 ÷ 4 = 25,500,257.75

If the quotient is a whole number, then 4 and 25,500,257.75 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:

1 102,001,031
-1 102,001,031
Keep dividing by the next highest number until you cannot divide anymore.

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

11143894739792,4233,82726,65342,097104,189215,6471,146,0792,372,1179,272,821102,001,031
-1-11-43-89-473-979-2,423-3,827-26,653-42,097-104,189-215,647-1,146,079-2,372,117-9,272,821-102,001,031

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