Q: What are the factor combinations of the number 40,204,465?

 A:
Positive:   1 x 402044655 x 80408937 x 574349535 x 1148699443 x 907552215 x 181512593 x 155053101 x 12965
Negative: -1 x -40204465-5 x -8040893-7 x -5743495-35 x -1148699-443 x -90755-2215 x -18151-2593 x -15505-3101 x -12965


How do I find the factor combinations of the number 40,204,465?

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 40,204,465, 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 40,204,465
-1 -40,204,465

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 40,204,465.

Example:
1 x 40,204,465 = 40,204,465
and
-1 x -40,204,465 = 40,204,465
Notice both answers equal 40,204,465

With that explanation out of the way, let's continue. Next, we take the number 40,204,465 and divide it by 2:

40,204,465 ÷ 2 = 20,102,232.5

If the quotient is a whole number, then 2 and 20,102,232.5 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 40,204,465
-1 -40,204,465

Now, we try dividing 40,204,465 by 3:

40,204,465 ÷ 3 = 13,401,488.3333

If the quotient is a whole number, then 3 and 13,401,488.3333 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 40,204,465
-1 -40,204,465

Let's try dividing by 4:

40,204,465 ÷ 4 = 10,051,116.25

If the quotient is a whole number, then 4 and 10,051,116.25 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 40,204,465
-1 40,204,465
Keep dividing by the next highest number until you cannot divide anymore.

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

157354432,2152,5933,10112,96515,50518,15190,7551,148,6995,743,4958,040,89340,204,465
-1-5-7-35-443-2,215-2,593-3,101-12,965-15,505-18,151-90,755-1,148,699-5,743,495-8,040,893-40,204,465

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