Q: What are the factor combinations of the number 35,735,142?

 A:
Positive:   1 x 357351422 x 178675713 x 119117146 x 595585761 x 585822122 x 292911163 x 219234183 x 195274326 x 109617366 x 97637489 x 73078599 x 59658978 x 365391198 x 298291797 x 198863594 x 9943
Negative: -1 x -35735142-2 x -17867571-3 x -11911714-6 x -5955857-61 x -585822-122 x -292911-163 x -219234-183 x -195274-326 x -109617-366 x -97637-489 x -73078-599 x -59658-978 x -36539-1198 x -29829-1797 x -19886-3594 x -9943


How do I find the factor combinations of the number 35,735,142?

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 35,735,142, 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 35,735,142
-1 -35,735,142

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 35,735,142.

Example:
1 x 35,735,142 = 35,735,142
and
-1 x -35,735,142 = 35,735,142
Notice both answers equal 35,735,142

With that explanation out of the way, let's continue. Next, we take the number 35,735,142 and divide it by 2:

35,735,142 ÷ 2 = 17,867,571

If the quotient is a whole number, then 2 and 17,867,571 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 17,867,571 35,735,142
-1 -2 -17,867,571 -35,735,142

Now, we try dividing 35,735,142 by 3:

35,735,142 ÷ 3 = 11,911,714

If the quotient is a whole number, then 3 and 11,911,714 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 11,911,714 17,867,571 35,735,142
-1 -2 -3 -11,911,714 -17,867,571 -35,735,142

Let's try dividing by 4:

35,735,142 ÷ 4 = 8,933,785.5

If the quotient is a whole number, then 4 and 8,933,785.5 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 2 3 11,911,714 17,867,571 35,735,142
-1 -2 -3 -11,911,714 -17,867,571 35,735,142
Keep dividing by the next highest number until you cannot divide anymore.

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

1236611221631833263664895999781,1981,7973,5949,94319,88629,82936,53959,65873,07897,637109,617195,274219,234292,911585,8225,955,85711,911,71417,867,57135,735,142
-1-2-3-6-61-122-163-183-326-366-489-599-978-1,198-1,797-3,594-9,943-19,886-29,829-36,539-59,658-73,078-97,637-109,617-195,274-219,234-292,911-585,822-5,955,857-11,911,714-17,867,571-35,735,142

More Examples

Here are some more numbers to try:

35,735,14035,735,14135,735,14335,735,144
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