Q: What are the factor combinations of the number 350,075?

 A:
Positive:   1 x 3500755 x 7001511 x 3182519 x 1842525 x 1400355 x 636567 x 522595 x 3685209 x 1675275 x 1273335 x 1045475 x 737
Negative: -1 x -350075-5 x -70015-11 x -31825-19 x -18425-25 x -14003-55 x -6365-67 x -5225-95 x -3685-209 x -1675-275 x -1273-335 x -1045-475 x -737


How do I find the factor combinations of the number 350,075?

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 350,075, 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.

1 350,075
-1 -350,075

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 350,075.

Example:
1 x 350,075 = 350,075
and
-1 x -350,075 = 350,075
Notice both answers equal 350,075

With that explanation out of the way, let's continue. Next, we take the number 350,075 and divide it by 2:

350,075 ÷ 2 = 175,037.5

If the quotient is a whole number, then 2 and 175,037.5 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:

1 350,075
-1 -350,075

Now, we try dividing 350,075 by 3:

350,075 ÷ 3 = 116,691.6667

If the quotient is a whole number, then 3 and 116,691.6667 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:

1 350,075
-1 -350,075

Let's try dividing by 4:

350,075 ÷ 4 = 87,518.75

If the quotient is a whole number, then 4 and 87,518.75 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:

1 350,075
-1 350,075
Keep dividing by the next highest number until you cannot divide anymore.

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

151119255567952092753354757371,0451,2731,6753,6855,2256,36514,00318,42531,82570,015350,075
-1-5-11-19-25-55-67-95-209-275-335-475-737-1,045-1,273-1,675-3,685-5,225-6,365-14,003-18,425-31,825-70,015-350,075

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