Q: What are the factor combinations of the number 460,748,005?

 A:
Positive:   1 x 4607480055 x 9214960119 x 2424989595 x 48499791789 x 2575452711 x 1699558945 x 5150913555 x 33991
Negative: -1 x -460748005-5 x -92149601-19 x -24249895-95 x -4849979-1789 x -257545-2711 x -169955-8945 x -51509-13555 x -33991


How do I find the factor combinations of the number 460,748,005?

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 460,748,005, 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.

1 460,748,005
-1 -460,748,005

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 460,748,005.

Example:
1 x 460,748,005 = 460,748,005
and
-1 x -460,748,005 = 460,748,005
Notice both answers equal 460,748,005

With that explanation out of the way, let's continue. Next, we take the number 460,748,005 and divide it by 2:

460,748,005 ÷ 2 = 230,374,002.5

If the quotient is a whole number, then 2 and 230,374,002.5 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:

1 460,748,005
-1 -460,748,005

Now, we try dividing 460,748,005 by 3:

460,748,005 ÷ 3 = 153,582,668.3333

If the quotient is a whole number, then 3 and 153,582,668.3333 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:

1 460,748,005
-1 -460,748,005

Let's try dividing by 4:

460,748,005 ÷ 4 = 115,187,001.25

If the quotient is a whole number, then 4 and 115,187,001.25 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:

1 460,748,005
-1 460,748,005
Keep dividing by the next highest number until you cannot divide anymore.

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

1519951,7892,7118,94513,55533,99151,509169,955257,5454,849,97924,249,89592,149,601460,748,005
-1-5-19-95-1,789-2,711-8,945-13,555-33,991-51,509-169,955-257,545-4,849,979-24,249,895-92,149,601-460,748,005

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