Q: What are the factor combinations of the number 23,224,140?

 A:
Positive:   1 x 232241402 x 116120703 x 77413804 x 58060355 x 46448286 x 38706909 x 258046010 x 232241412 x 193534515 x 154827618 x 129023020 x 116120730 x 77413836 x 64511545 x 51609260 x 38706990 x 258046180 x 129023
Negative: -1 x -23224140-2 x -11612070-3 x -7741380-4 x -5806035-5 x -4644828-6 x -3870690-9 x -2580460-10 x -2322414-12 x -1935345-15 x -1548276-18 x -1290230-20 x -1161207-30 x -774138-36 x -645115-45 x -516092-60 x -387069-90 x -258046-180 x -129023


How do I find the factor combinations of the number 23,224,140?

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 23,224,140, 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 23,224,140
-1 -23,224,140

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 23,224,140.

Example:
1 x 23,224,140 = 23,224,140
and
-1 x -23,224,140 = 23,224,140
Notice both answers equal 23,224,140

With that explanation out of the way, let's continue. Next, we take the number 23,224,140 and divide it by 2:

23,224,140 ÷ 2 = 11,612,070

If the quotient is a whole number, then 2 and 11,612,070 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 11,612,070 23,224,140
-1 -2 -11,612,070 -23,224,140

Now, we try dividing 23,224,140 by 3:

23,224,140 ÷ 3 = 7,741,380

If the quotient is a whole number, then 3 and 7,741,380 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 7,741,380 11,612,070 23,224,140
-1 -2 -3 -7,741,380 -11,612,070 -23,224,140

Let's try dividing by 4:

23,224,140 ÷ 4 = 5,806,035

If the quotient is a whole number, then 4 and 5,806,035 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 5,806,035 7,741,380 11,612,070 23,224,140
-1 -2 -3 -4 -5,806,035 -7,741,380 -11,612,070 23,224,140
Keep dividing by the next highest number until you cannot divide anymore.

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

123456910121518203036456090180129,023258,046387,069516,092645,115774,1381,161,2071,290,2301,548,2761,935,3452,322,4142,580,4603,870,6904,644,8285,806,0357,741,38011,612,07023,224,140
-1-2-3-4-5-6-9-10-12-15-18-20-30-36-45-60-90-180-129,023-258,046-387,069-516,092-645,115-774,138-1,161,207-1,290,230-1,548,276-1,935,345-2,322,414-2,580,460-3,870,690-4,644,828-5,806,035-7,741,380-11,612,070-23,224,140

More Examples

Here are some more numbers to try:

23,224,13823,224,13923,224,14123,224,142
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