Q: What are the factor combinations of the number 144,258,565?

 A:
Positive:   1 x 1442585655 x 2885171311 x 1311441555 x 262288383 x 1738055415 x 347611913 x 1580054565 x 31601
Negative: -1 x -144258565-5 x -28851713-11 x -13114415-55 x -2622883-83 x -1738055-415 x -347611-913 x -158005-4565 x -31601


How do I find the factor combinations of the number 144,258,565?

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 144,258,565, 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.

1 144,258,565
-1 -144,258,565

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 144,258,565.

Example:
1 x 144,258,565 = 144,258,565
and
-1 x -144,258,565 = 144,258,565
Notice both answers equal 144,258,565

With that explanation out of the way, let's continue. Next, we take the number 144,258,565 and divide it by 2:

144,258,565 ÷ 2 = 72,129,282.5

If the quotient is a whole number, then 2 and 72,129,282.5 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:

1 144,258,565
-1 -144,258,565

Now, we try dividing 144,258,565 by 3:

144,258,565 ÷ 3 = 48,086,188.3333

If the quotient is a whole number, then 3 and 48,086,188.3333 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:

1 144,258,565
-1 -144,258,565

Let's try dividing by 4:

144,258,565 ÷ 4 = 36,064,641.25

If the quotient is a whole number, then 4 and 36,064,641.25 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:

1 144,258,565
-1 144,258,565
Keep dividing by the next highest number until you cannot divide anymore.

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

151155834159134,56531,601158,005347,6111,738,0552,622,88313,114,41528,851,713144,258,565
-1-5-11-55-83-415-913-4,565-31,601-158,005-347,611-1,738,055-2,622,883-13,114,415-28,851,713-144,258,565

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