Q: What are the factor combinations of the number 104,210,401?

 A:
Positive:   1 x 10421040123 x 453088779 x 131911983 x 1255547691 x 1508111817 x 573531909 x 545896557 x 15893
Negative: -1 x -104210401-23 x -4530887-79 x -1319119-83 x -1255547-691 x -150811-1817 x -57353-1909 x -54589-6557 x -15893


How do I find the factor combinations of the number 104,210,401?

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 104,210,401, 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.

1 104,210,401
-1 -104,210,401

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 104,210,401.

Example:
1 x 104,210,401 = 104,210,401
and
-1 x -104,210,401 = 104,210,401
Notice both answers equal 104,210,401

With that explanation out of the way, let's continue. Next, we take the number 104,210,401 and divide it by 2:

104,210,401 ÷ 2 = 52,105,200.5

If the quotient is a whole number, then 2 and 52,105,200.5 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:

1 104,210,401
-1 -104,210,401

Now, we try dividing 104,210,401 by 3:

104,210,401 ÷ 3 = 34,736,800.3333

If the quotient is a whole number, then 3 and 34,736,800.3333 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:

1 104,210,401
-1 -104,210,401

Let's try dividing by 4:

104,210,401 ÷ 4 = 26,052,600.25

If the quotient is a whole number, then 4 and 26,052,600.25 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:

1 104,210,401
-1 104,210,401
Keep dividing by the next highest number until you cannot divide anymore.

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

12379836911,8171,9096,55715,89354,58957,353150,8111,255,5471,319,1194,530,887104,210,401
-1-23-79-83-691-1,817-1,909-6,557-15,893-54,589-57,353-150,811-1,255,547-1,319,119-4,530,887-104,210,401

More Examples

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