Q: What are the factor combinations of the number 675,015,013?

 A:
Positive:   1 x 67501501337 x 1824364973 x 924678183 x 81327112701 x 2499133011 x 2241833071 x 2198036059 x 111407
Negative: -1 x -675015013-37 x -18243649-73 x -9246781-83 x -8132711-2701 x -249913-3011 x -224183-3071 x -219803-6059 x -111407


How do I find the factor combinations of the number 675,015,013?

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 675,015,013, 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.

1 675,015,013
-1 -675,015,013

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 675,015,013.

Example:
1 x 675,015,013 = 675,015,013
and
-1 x -675,015,013 = 675,015,013
Notice both answers equal 675,015,013

With that explanation out of the way, let's continue. Next, we take the number 675,015,013 and divide it by 2:

675,015,013 ÷ 2 = 337,507,506.5

If the quotient is a whole number, then 2 and 337,507,506.5 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:

1 675,015,013
-1 -675,015,013

Now, we try dividing 675,015,013 by 3:

675,015,013 ÷ 3 = 225,005,004.3333

If the quotient is a whole number, then 3 and 225,005,004.3333 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:

1 675,015,013
-1 -675,015,013

Let's try dividing by 4:

675,015,013 ÷ 4 = 168,753,753.25

If the quotient is a whole number, then 4 and 168,753,753.25 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:

1 675,015,013
-1 675,015,013
Keep dividing by the next highest number until you cannot divide anymore.

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

13773832,7013,0113,0716,059111,407219,803224,183249,9138,132,7119,246,78118,243,649675,015,013
-1-37-73-83-2,701-3,011-3,071-6,059-111,407-219,803-224,183-249,913-8,132,711-9,246,781-18,243,649-675,015,013

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