Q: What are the factor combinations of the number 300,122,220?

 A:
Positive:   1 x 3001222202 x 1500611103 x 1000407404 x 750305555 x 600244446 x 5002037010 x 3001222212 x 2501018515 x 2000814820 x 1500611130 x 1000407460 x 5002037467 x 642660934 x 3213301401 x 2142201868 x 1606652335 x 1285322802 x 1071104670 x 642665604 x 535557005 x 428449340 x 3213310711 x 2802014010 x 21422
Negative: -1 x -300122220-2 x -150061110-3 x -100040740-4 x -75030555-5 x -60024444-6 x -50020370-10 x -30012222-12 x -25010185-15 x -20008148-20 x -15006111-30 x -10004074-60 x -5002037-467 x -642660-934 x -321330-1401 x -214220-1868 x -160665-2335 x -128532-2802 x -107110-4670 x -64266-5604 x -53555-7005 x -42844-9340 x -32133-10711 x -28020-14010 x -21422


How do I find the factor combinations of the number 300,122,220?

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 300,122,220, 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.

1 300,122,220
-1 -300,122,220

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 300,122,220.

Example:
1 x 300,122,220 = 300,122,220
and
-1 x -300,122,220 = 300,122,220
Notice both answers equal 300,122,220

With that explanation out of the way, let's continue. Next, we take the number 300,122,220 and divide it by 2:

300,122,220 ÷ 2 = 150,061,110

If the quotient is a whole number, then 2 and 150,061,110 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 2 150,061,110 300,122,220
-1 -2 -150,061,110 -300,122,220

Now, we try dividing 300,122,220 by 3:

300,122,220 ÷ 3 = 100,040,740

If the quotient is a whole number, then 3 and 100,040,740 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 3 100,040,740 150,061,110 300,122,220
-1 -2 -3 -100,040,740 -150,061,110 -300,122,220

Let's try dividing by 4:

300,122,220 ÷ 4 = 75,030,555

If the quotient is a whole number, then 4 and 75,030,555 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 75,030,555 100,040,740 150,061,110 300,122,220
-1 -2 -3 -4 -75,030,555 -100,040,740 -150,061,110 300,122,220
Keep dividing by the next highest number until you cannot divide anymore.

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

1234561012152030604679341,4011,8682,3352,8024,6705,6047,0059,34010,71114,01021,42228,02032,13342,84453,55564,266107,110128,532160,665214,220321,330642,6605,002,03710,004,07415,006,11120,008,14825,010,18530,012,22250,020,37060,024,44475,030,555100,040,740150,061,110300,122,220
-1-2-3-4-5-6-10-12-15-20-30-60-467-934-1,401-1,868-2,335-2,802-4,670-5,604-7,005-9,340-10,711-14,010-21,422-28,020-32,133-42,844-53,555-64,266-107,110-128,532-160,665-214,220-321,330-642,660-5,002,037-10,004,074-15,006,111-20,008,148-25,010,185-30,012,222-50,020,370-60,024,444-75,030,555-100,040,740-150,061,110-300,122,220

More Examples

Here are some more numbers to try:

300,122,218300,122,219300,122,221300,122,222
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