Q: What are the factor combinations of the number 106,216,404?

 A:
Positive:   1 x 1062164042 x 531082023 x 354054684 x 265541016 x 177027347 x 1517377212 x 885136714 x 758688621 x 505792428 x 379344341 x 259064442 x 252896282 x 129532284 x 1264481123 x 863548164 x 647661246 x 431774287 x 370092492 x 215887574 x 185046861 x 1233641148 x 925231722 x 616823444 x 30841
Negative: -1 x -106216404-2 x -53108202-3 x -35405468-4 x -26554101-6 x -17702734-7 x -15173772-12 x -8851367-14 x -7586886-21 x -5057924-28 x -3793443-41 x -2590644-42 x -2528962-82 x -1295322-84 x -1264481-123 x -863548-164 x -647661-246 x -431774-287 x -370092-492 x -215887-574 x -185046-861 x -123364-1148 x -92523-1722 x -61682-3444 x -30841


How do I find the factor combinations of the number 106,216,404?

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 106,216,404, 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.

1 106,216,404
-1 -106,216,404

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 106,216,404.

Example:
1 x 106,216,404 = 106,216,404
and
-1 x -106,216,404 = 106,216,404
Notice both answers equal 106,216,404

With that explanation out of the way, let's continue. Next, we take the number 106,216,404 and divide it by 2:

106,216,404 ÷ 2 = 53,108,202

If the quotient is a whole number, then 2 and 53,108,202 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 53,108,202 106,216,404
-1 -2 -53,108,202 -106,216,404

Now, we try dividing 106,216,404 by 3:

106,216,404 ÷ 3 = 35,405,468

If the quotient is a whole number, then 3 and 35,405,468 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 35,405,468 53,108,202 106,216,404
-1 -2 -3 -35,405,468 -53,108,202 -106,216,404

Let's try dividing by 4:

106,216,404 ÷ 4 = 26,554,101

If the quotient is a whole number, then 4 and 26,554,101 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 26,554,101 35,405,468 53,108,202 106,216,404
-1 -2 -3 -4 -26,554,101 -35,405,468 -53,108,202 106,216,404
Keep dividing by the next highest number until you cannot divide anymore.

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

12346712142128414282841231642462874925748611,1481,7223,44430,84161,68292,523123,364185,046215,887370,092431,774647,661863,5481,264,4811,295,3222,528,9622,590,6443,793,4435,057,9247,586,8868,851,36715,173,77217,702,73426,554,10135,405,46853,108,202106,216,404
-1-2-3-4-6-7-12-14-21-28-41-42-82-84-123-164-246-287-492-574-861-1,148-1,722-3,444-30,841-61,682-92,523-123,364-185,046-215,887-370,092-431,774-647,661-863,548-1,264,481-1,295,322-2,528,962-2,590,644-3,793,443-5,057,924-7,586,886-8,851,367-15,173,772-17,702,734-26,554,101-35,405,468-53,108,202-106,216,404

More Examples

Here are some more numbers to try:

106,216,402106,216,403106,216,405106,216,406
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