Q: What are the factor combinations of the number 46,301,365?

 A:
Positive:   1 x 463013655 x 926027311 x 420921555 x 841843577 x 802451459 x 317352885 x 160496347 x 7295
Negative: -1 x -46301365-5 x -9260273-11 x -4209215-55 x -841843-577 x -80245-1459 x -31735-2885 x -16049-6347 x -7295


How do I find the factor combinations of the number 46,301,365?

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 46,301,365, 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 46,301,365
-1 -46,301,365

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 46,301,365.

Example:
1 x 46,301,365 = 46,301,365
and
-1 x -46,301,365 = 46,301,365
Notice both answers equal 46,301,365

With that explanation out of the way, let's continue. Next, we take the number 46,301,365 and divide it by 2:

46,301,365 ÷ 2 = 23,150,682.5

If the quotient is a whole number, then 2 and 23,150,682.5 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 46,301,365
-1 -46,301,365

Now, we try dividing 46,301,365 by 3:

46,301,365 ÷ 3 = 15,433,788.3333

If the quotient is a whole number, then 3 and 15,433,788.3333 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 46,301,365
-1 -46,301,365

Let's try dividing by 4:

46,301,365 ÷ 4 = 11,575,341.25

If the quotient is a whole number, then 4 and 11,575,341.25 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 46,301,365
-1 46,301,365
Keep dividing by the next highest number until you cannot divide anymore.

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

1511555771,4592,8856,3477,29516,04931,73580,245841,8434,209,2159,260,27346,301,365
-1-5-11-55-577-1,459-2,885-6,347-7,295-16,049-31,735-80,245-841,843-4,209,215-9,260,273-46,301,365

More Examples

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