Q: What are the factor combinations of the number 40,210,225?

 A:
Positive:   1 x 402102255 x 804204511 x 365547525 x 160840955 x 73109573 x 550825275 x 146219365 x 110165803 x 500751825 x 220332003 x 200754015 x 10015
Negative: -1 x -40210225-5 x -8042045-11 x -3655475-25 x -1608409-55 x -731095-73 x -550825-275 x -146219-365 x -110165-803 x -50075-1825 x -22033-2003 x -20075-4015 x -10015


How do I find the factor combinations of the number 40,210,225?

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 40,210,225, 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 40,210,225
-1 -40,210,225

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 40,210,225.

Example:
1 x 40,210,225 = 40,210,225
and
-1 x -40,210,225 = 40,210,225
Notice both answers equal 40,210,225

With that explanation out of the way, let's continue. Next, we take the number 40,210,225 and divide it by 2:

40,210,225 ÷ 2 = 20,105,112.5

If the quotient is a whole number, then 2 and 20,105,112.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 40,210,225
-1 -40,210,225

Now, we try dividing 40,210,225 by 3:

40,210,225 ÷ 3 = 13,403,408.3333

If the quotient is a whole number, then 3 and 13,403,408.3333 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 40,210,225
-1 -40,210,225

Let's try dividing by 4:

40,210,225 ÷ 4 = 10,052,556.25

If the quotient is a whole number, then 4 and 10,052,556.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 40,210,225
-1 40,210,225
Keep dividing by the next highest number until you cannot divide anymore.

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

15112555732753658031,8252,0034,01510,01520,07522,03350,075110,165146,219550,825731,0951,608,4093,655,4758,042,04540,210,225
-1-5-11-25-55-73-275-365-803-1,825-2,003-4,015-10,015-20,075-22,033-50,075-110,165-146,219-550,825-731,095-1,608,409-3,655,475-8,042,045-40,210,225

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