Q: What are the factor combinations of the number 402,223,451?

 A:
Positive:   1 x 4022234517 x 5746049317 x 23660203119 x 3380029401 x 10030512807 x 1432936817 x 590038429 x 47719
Negative: -1 x -402223451-7 x -57460493-17 x -23660203-119 x -3380029-401 x -1003051-2807 x -143293-6817 x -59003-8429 x -47719


How do I find the factor combinations of the number 402,223,451?

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 402,223,451, 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.

1 402,223,451
-1 -402,223,451

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 402,223,451.

Example:
1 x 402,223,451 = 402,223,451
and
-1 x -402,223,451 = 402,223,451
Notice both answers equal 402,223,451

With that explanation out of the way, let's continue. Next, we take the number 402,223,451 and divide it by 2:

402,223,451 ÷ 2 = 201,111,725.5

If the quotient is a whole number, then 2 and 201,111,725.5 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:

1 402,223,451
-1 -402,223,451

Now, we try dividing 402,223,451 by 3:

402,223,451 ÷ 3 = 134,074,483.6667

If the quotient is a whole number, then 3 and 134,074,483.6667 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:

1 402,223,451
-1 -402,223,451

Let's try dividing by 4:

402,223,451 ÷ 4 = 100,555,862.75

If the quotient is a whole number, then 4 and 100,555,862.75 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:

1 402,223,451
-1 402,223,451
Keep dividing by the next highest number until you cannot divide anymore.

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

17171194012,8076,8178,42947,71959,003143,2931,003,0513,380,02923,660,20357,460,493402,223,451
-1-7-17-119-401-2,807-6,817-8,429-47,719-59,003-143,293-1,003,051-3,380,029-23,660,203-57,460,493-402,223,451

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