Q: What are the factor combinations of the number 1,600,225?

 A:
Positive:   1 x 16002255 x 32004511 x 14547523 x 6957525 x 6400955 x 29095115 x 13915121 x 13225253 x 6325275 x 5819529 x 3025575 x 2783605 x 26451265 x 1265
Negative: -1 x -1600225-5 x -320045-11 x -145475-23 x -69575-25 x -64009-55 x -29095-115 x -13915-121 x -13225-253 x -6325-275 x -5819-529 x -3025-575 x -2783-605 x -2645-1265 x -1265


How do I find the factor combinations of the number 1,600,225?

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 1,600,225, 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 1,600,225
-1 -1,600,225

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 1,600,225.

Example:
1 x 1,600,225 = 1,600,225
and
-1 x -1,600,225 = 1,600,225
Notice both answers equal 1,600,225

With that explanation out of the way, let's continue. Next, we take the number 1,600,225 and divide it by 2:

1,600,225 ÷ 2 = 800,112.5

If the quotient is a whole number, then 2 and 800,112.5 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 1,600,225
-1 -1,600,225

Now, we try dividing 1,600,225 by 3:

1,600,225 ÷ 3 = 533,408.3333

If the quotient is a whole number, then 3 and 533,408.3333 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 1,600,225
-1 -1,600,225

Let's try dividing by 4:

1,600,225 ÷ 4 = 400,056.25

If the quotient is a whole number, then 4 and 400,056.25 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 1,600,225
-1 1,600,225
Keep dividing by the next highest number until you cannot divide anymore.

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

15112325551151212532755295756051,2652,6452,7833,0255,8196,32513,22513,91529,09564,00969,575145,475320,0451,600,225
-1-5-11-23-25-55-115-121-253-275-529-575-605-1,265-2,645-2,783-3,025-5,819-6,325-13,225-13,915-29,095-64,009-69,575-145,475-320,045-1,600,225

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