Q: What are the factor combinations of the number 450,275?

 A:
Positive:   1 x 4502755 x 900557 x 6432525 x 1801131 x 1452535 x 1286583 x 5425155 x 2905175 x 2573217 x 2075415 x 1085581 x 775
Negative: -1 x -450275-5 x -90055-7 x -64325-25 x -18011-31 x -14525-35 x -12865-83 x -5425-155 x -2905-175 x -2573-217 x -2075-415 x -1085-581 x -775


How do I find the factor combinations of the number 450,275?

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 450,275, 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.

1 450,275
-1 -450,275

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 450,275.

Example:
1 x 450,275 = 450,275
and
-1 x -450,275 = 450,275
Notice both answers equal 450,275

With that explanation out of the way, let's continue. Next, we take the number 450,275 and divide it by 2:

450,275 ÷ 2 = 225,137.5

If the quotient is a whole number, then 2 and 225,137.5 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:

1 450,275
-1 -450,275

Now, we try dividing 450,275 by 3:

450,275 ÷ 3 = 150,091.6667

If the quotient is a whole number, then 3 and 150,091.6667 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:

1 450,275
-1 -450,275

Let's try dividing by 4:

450,275 ÷ 4 = 112,568.75

If the quotient is a whole number, then 4 and 112,568.75 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:

1 450,275
-1 450,275
Keep dividing by the next highest number until you cannot divide anymore.

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

157253135831551752174155817751,0852,0752,5732,9055,42512,86514,52518,01164,32590,055450,275
-1-5-7-25-31-35-83-155-175-217-415-581-775-1,085-2,075-2,573-2,905-5,425-12,865-14,525-18,011-64,325-90,055-450,275

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