Q: What are the factor combinations of the number 35,044,429?

 A:
Positive:   1 x 350444297 x 500634717 x 2061437119 x 294491289 x 1212611019 x 343912023 x 173234913 x 7133
Negative: -1 x -35044429-7 x -5006347-17 x -2061437-119 x -294491-289 x -121261-1019 x -34391-2023 x -17323-4913 x -7133


How do I find the factor combinations of the number 35,044,429?

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 35,044,429, 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 35,044,429
-1 -35,044,429

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 35,044,429.

Example:
1 x 35,044,429 = 35,044,429
and
-1 x -35,044,429 = 35,044,429
Notice both answers equal 35,044,429

With that explanation out of the way, let's continue. Next, we take the number 35,044,429 and divide it by 2:

35,044,429 ÷ 2 = 17,522,214.5

If the quotient is a whole number, then 2 and 17,522,214.5 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 35,044,429
-1 -35,044,429

Now, we try dividing 35,044,429 by 3:

35,044,429 ÷ 3 = 11,681,476.3333

If the quotient is a whole number, then 3 and 11,681,476.3333 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 35,044,429
-1 -35,044,429

Let's try dividing by 4:

35,044,429 ÷ 4 = 8,761,107.25

If the quotient is a whole number, then 4 and 8,761,107.25 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 35,044,429
-1 35,044,429
Keep dividing by the next highest number until you cannot divide anymore.

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

17171192891,0192,0234,9137,13317,32334,391121,261294,4912,061,4375,006,34735,044,429
-1-7-17-119-289-1,019-2,023-4,913-7,133-17,323-34,391-121,261-294,491-2,061,437-5,006,347-35,044,429

More Examples

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