Q: What are the factor combinations of the number 404,142,145?

 A:
Positive:   1 x 4041421455 x 8082842911 x 3674019555 x 73480391361 x 2969455399 x 748556805 x 5938914971 x 26995
Negative: -1 x -404142145-5 x -80828429-11 x -36740195-55 x -7348039-1361 x -296945-5399 x -74855-6805 x -59389-14971 x -26995


How do I find the factor combinations of the number 404,142,145?

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 404,142,145, 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.

1 404,142,145
-1 -404,142,145

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 404,142,145.

Example:
1 x 404,142,145 = 404,142,145
and
-1 x -404,142,145 = 404,142,145
Notice both answers equal 404,142,145

With that explanation out of the way, let's continue. Next, we take the number 404,142,145 and divide it by 2:

404,142,145 ÷ 2 = 202,071,072.5

If the quotient is a whole number, then 2 and 202,071,072.5 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:

1 404,142,145
-1 -404,142,145

Now, we try dividing 404,142,145 by 3:

404,142,145 ÷ 3 = 134,714,048.3333

If the quotient is a whole number, then 3 and 134,714,048.3333 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:

1 404,142,145
-1 -404,142,145

Let's try dividing by 4:

404,142,145 ÷ 4 = 101,035,536.25

If the quotient is a whole number, then 4 and 101,035,536.25 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:

1 404,142,145
-1 404,142,145
Keep dividing by the next highest number until you cannot divide anymore.

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

1511551,3615,3996,80514,97126,99559,38974,855296,9457,348,03936,740,19580,828,429404,142,145
-1-5-11-55-1,361-5,399-6,805-14,971-26,995-59,389-74,855-296,945-7,348,039-36,740,195-80,828,429-404,142,145

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