Q: What are the factor combinations of the number 40,501,128?

 A:
Positive:   1 x 405011282 x 202505643 x 135003764 x 101252826 x 67501888 x 506264112 x 337509424 x 168754731 x 130648862 x 65324493 x 435496124 x 326622186 x 217748248 x 163311372 x 108874744 x 54437
Negative: -1 x -40501128-2 x -20250564-3 x -13500376-4 x -10125282-6 x -6750188-8 x -5062641-12 x -3375094-24 x -1687547-31 x -1306488-62 x -653244-93 x -435496-124 x -326622-186 x -217748-248 x -163311-372 x -108874-744 x -54437


How do I find the factor combinations of the number 40,501,128?

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 40,501,128, 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 40,501,128
-1 -40,501,128

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 40,501,128.

Example:
1 x 40,501,128 = 40,501,128
and
-1 x -40,501,128 = 40,501,128
Notice both answers equal 40,501,128

With that explanation out of the way, let's continue. Next, we take the number 40,501,128 and divide it by 2:

40,501,128 ÷ 2 = 20,250,564

If the quotient is a whole number, then 2 and 20,250,564 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 20,250,564 40,501,128
-1 -2 -20,250,564 -40,501,128

Now, we try dividing 40,501,128 by 3:

40,501,128 ÷ 3 = 13,500,376

If the quotient is a whole number, then 3 and 13,500,376 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 13,500,376 20,250,564 40,501,128
-1 -2 -3 -13,500,376 -20,250,564 -40,501,128

Let's try dividing by 4:

40,501,128 ÷ 4 = 10,125,282

If the quotient is a whole number, then 4 and 10,125,282 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 4 10,125,282 13,500,376 20,250,564 40,501,128
-1 -2 -3 -4 -10,125,282 -13,500,376 -20,250,564 40,501,128
Keep dividing by the next highest number until you cannot divide anymore.

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

123468122431629312418624837274454,437108,874163,311217,748326,622435,496653,2441,306,4881,687,5473,375,0945,062,6416,750,18810,125,28213,500,37620,250,56440,501,128
-1-2-3-4-6-8-12-24-31-62-93-124-186-248-372-744-54,437-108,874-163,311-217,748-326,622-435,496-653,244-1,306,488-1,687,547-3,375,094-5,062,641-6,750,188-10,125,282-13,500,376-20,250,564-40,501,128

More Examples

Here are some more numbers to try:

40,501,12640,501,12740,501,12940,501,130
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