Q: What are the factor combinations of the number 401,353,225?

 A:
Positive:   1 x 4013532255 x 802706457 x 5733617513 x 3087332525 x 1605412935 x 1146723565 x 617466591 x 4410475175 x 2293447325 x 1234933455 x 8820952275 x 176419
Negative: -1 x -401353225-5 x -80270645-7 x -57336175-13 x -30873325-25 x -16054129-35 x -11467235-65 x -6174665-91 x -4410475-175 x -2293447-325 x -1234933-455 x -882095-2275 x -176419


How do I find the factor combinations of the number 401,353,225?

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 401,353,225, 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.

1 401,353,225
-1 -401,353,225

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 401,353,225.

Example:
1 x 401,353,225 = 401,353,225
and
-1 x -401,353,225 = 401,353,225
Notice both answers equal 401,353,225

With that explanation out of the way, let's continue. Next, we take the number 401,353,225 and divide it by 2:

401,353,225 ÷ 2 = 200,676,612.5

If the quotient is a whole number, then 2 and 200,676,612.5 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:

1 401,353,225
-1 -401,353,225

Now, we try dividing 401,353,225 by 3:

401,353,225 ÷ 3 = 133,784,408.3333

If the quotient is a whole number, then 3 and 133,784,408.3333 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:

1 401,353,225
-1 -401,353,225

Let's try dividing by 4:

401,353,225 ÷ 4 = 100,338,306.25

If the quotient is a whole number, then 4 and 100,338,306.25 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:

1 401,353,225
-1 401,353,225
Keep dividing by the next highest number until you cannot divide anymore.

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

15713253565911753254552,275176,419882,0951,234,9332,293,4474,410,4756,174,66511,467,23516,054,12930,873,32557,336,17580,270,645401,353,225
-1-5-7-13-25-35-65-91-175-325-455-2,275-176,419-882,095-1,234,933-2,293,447-4,410,475-6,174,665-11,467,235-16,054,129-30,873,325-57,336,175-80,270,645-401,353,225

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