Q: What are the factor combinations of the number 321,403,140?

 A:
Positive:   1 x 3214031402 x 1607015703 x 1071343804 x 803507855 x 642806286 x 535671909 x 3571146010 x 3214031412 x 2678359515 x 2142687618 x 1785573020 x 1607015727 x 1190382030 x 1071343836 x 892786545 x 714229254 x 595191060 x 535671981 x 396794090 x 3571146108 x 2975955135 x 2380764162 x 1983970180 x 1785573270 x 1190382324 x 991985405 x 793588540 x 595191810 x 3967941620 x 198397
Negative: -1 x -321403140-2 x -160701570-3 x -107134380-4 x -80350785-5 x -64280628-6 x -53567190-9 x -35711460-10 x -32140314-12 x -26783595-15 x -21426876-18 x -17855730-20 x -16070157-27 x -11903820-30 x -10713438-36 x -8927865-45 x -7142292-54 x -5951910-60 x -5356719-81 x -3967940-90 x -3571146-108 x -2975955-135 x -2380764-162 x -1983970-180 x -1785573-270 x -1190382-324 x -991985-405 x -793588-540 x -595191-810 x -396794-1620 x -198397


How do I find the factor combinations of the number 321,403,140?

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 321,403,140, 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.

1 321,403,140
-1 -321,403,140

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 321,403,140.

Example:
1 x 321,403,140 = 321,403,140
and
-1 x -321,403,140 = 321,403,140
Notice both answers equal 321,403,140

With that explanation out of the way, let's continue. Next, we take the number 321,403,140 and divide it by 2:

321,403,140 ÷ 2 = 160,701,570

If the quotient is a whole number, then 2 and 160,701,570 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 2 160,701,570 321,403,140
-1 -2 -160,701,570 -321,403,140

Now, we try dividing 321,403,140 by 3:

321,403,140 ÷ 3 = 107,134,380

If the quotient is a whole number, then 3 and 107,134,380 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 3 107,134,380 160,701,570 321,403,140
-1 -2 -3 -107,134,380 -160,701,570 -321,403,140

Let's try dividing by 4:

321,403,140 ÷ 4 = 80,350,785

If the quotient is a whole number, then 4 and 80,350,785 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 80,350,785 107,134,380 160,701,570 321,403,140
-1 -2 -3 -4 -80,350,785 -107,134,380 -160,701,570 321,403,140
Keep dividing by the next highest number until you cannot divide anymore.

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

1234569101215182027303645546081901081351621802703244055408101,620198,397396,794595,191793,588991,9851,190,3821,785,5731,983,9702,380,7642,975,9553,571,1463,967,9405,356,7195,951,9107,142,2928,927,86510,713,43811,903,82016,070,15717,855,73021,426,87626,783,59532,140,31435,711,46053,567,19064,280,62880,350,785107,134,380160,701,570321,403,140
-1-2-3-4-5-6-9-10-12-15-18-20-27-30-36-45-54-60-81-90-108-135-162-180-270-324-405-540-810-1,620-198,397-396,794-595,191-793,588-991,985-1,190,382-1,785,573-1,983,970-2,380,764-2,975,955-3,571,146-3,967,940-5,356,719-5,951,910-7,142,292-8,927,865-10,713,438-11,903,820-16,070,157-17,855,730-21,426,876-26,783,595-32,140,314-35,711,460-53,567,190-64,280,628-80,350,785-107,134,380-160,701,570-321,403,140

More Examples

Here are some more numbers to try:

321,403,138321,403,139321,403,141321,403,142
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