Q: What are the factor combinations of the number 42,031,429?

 A:
Positive:   1 x 4203142911 x 382103917 x 247243773 x 575773187 x 224767803 x 523431241 x 338693079 x 13651
Negative: -1 x -42031429-11 x -3821039-17 x -2472437-73 x -575773-187 x -224767-803 x -52343-1241 x -33869-3079 x -13651


How do I find the factor combinations of the number 42,031,429?

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 42,031,429, 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 42,031,429
-1 -42,031,429

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 42,031,429.

Example:
1 x 42,031,429 = 42,031,429
and
-1 x -42,031,429 = 42,031,429
Notice both answers equal 42,031,429

With that explanation out of the way, let's continue. Next, we take the number 42,031,429 and divide it by 2:

42,031,429 ÷ 2 = 21,015,714.5

If the quotient is a whole number, then 2 and 21,015,714.5 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 42,031,429
-1 -42,031,429

Now, we try dividing 42,031,429 by 3:

42,031,429 ÷ 3 = 14,010,476.3333

If the quotient is a whole number, then 3 and 14,010,476.3333 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 42,031,429
-1 -42,031,429

Let's try dividing by 4:

42,031,429 ÷ 4 = 10,507,857.25

If the quotient is a whole number, then 4 and 10,507,857.25 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 42,031,429
-1 42,031,429
Keep dividing by the next highest number until you cannot divide anymore.

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

11117731878031,2413,07913,65133,86952,343224,767575,7732,472,4373,821,03942,031,429
-1-11-17-73-187-803-1,241-3,079-13,651-33,869-52,343-224,767-575,773-2,472,437-3,821,039-42,031,429

More Examples

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