Q: What are the factor combinations of the number 145,145?

 A:
Positive:   1 x 1451455 x 290297 x 2073511 x 1319513 x 1116529 x 500535 x 414755 x 263965 x 223377 x 188591 x 1595143 x 1015145 x 1001203 x 715319 x 455377 x 385
Negative: -1 x -145145-5 x -29029-7 x -20735-11 x -13195-13 x -11165-29 x -5005-35 x -4147-55 x -2639-65 x -2233-77 x -1885-91 x -1595-143 x -1015-145 x -1001-203 x -715-319 x -455-377 x -385


How do I find the factor combinations of the number 145,145?

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 145,145, 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.

1 145,145
-1 -145,145

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 145,145.

Example:
1 x 145,145 = 145,145
and
-1 x -145,145 = 145,145
Notice both answers equal 145,145

With that explanation out of the way, let's continue. Next, we take the number 145,145 and divide it by 2:

145,145 ÷ 2 = 72,572.5

If the quotient is a whole number, then 2 and 72,572.5 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:

1 145,145
-1 -145,145

Now, we try dividing 145,145 by 3:

145,145 ÷ 3 = 48,381.6667

If the quotient is a whole number, then 3 and 48,381.6667 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:

1 145,145
-1 -145,145

Let's try dividing by 4:

145,145 ÷ 4 = 36,286.25

If the quotient is a whole number, then 4 and 36,286.25 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:

1 145,145
-1 145,145
Keep dividing by the next highest number until you cannot divide anymore.

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

15711132935556577911431452033193773854557151,0011,0151,5951,8852,2332,6394,1475,00511,16513,19520,73529,029145,145
-1-5-7-11-13-29-35-55-65-77-91-143-145-203-319-377-385-455-715-1,001-1,015-1,595-1,885-2,233-2,639-4,147-5,005-11,165-13,195-20,735-29,029-145,145

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