Q: What are the factor combinations of the number 103,525,165?

 A:
Positive:   1 x 1035251655 x 2070503353 x 1953305241 x 429565265 x 3906611205 x 859131621 x 638658105 x 12773
Negative: -1 x -103525165-5 x -20705033-53 x -1953305-241 x -429565-265 x -390661-1205 x -85913-1621 x -63865-8105 x -12773


How do I find the factor combinations of the number 103,525,165?

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 103,525,165, 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.

1 103,525,165
-1 -103,525,165

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 103,525,165.

Example:
1 x 103,525,165 = 103,525,165
and
-1 x -103,525,165 = 103,525,165
Notice both answers equal 103,525,165

With that explanation out of the way, let's continue. Next, we take the number 103,525,165 and divide it by 2:

103,525,165 ÷ 2 = 51,762,582.5

If the quotient is a whole number, then 2 and 51,762,582.5 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:

1 103,525,165
-1 -103,525,165

Now, we try dividing 103,525,165 by 3:

103,525,165 ÷ 3 = 34,508,388.3333

If the quotient is a whole number, then 3 and 34,508,388.3333 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:

1 103,525,165
-1 -103,525,165

Let's try dividing by 4:

103,525,165 ÷ 4 = 25,881,291.25

If the quotient is a whole number, then 4 and 25,881,291.25 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:

1 103,525,165
-1 103,525,165
Keep dividing by the next highest number until you cannot divide anymore.

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

15532412651,2051,6218,10512,77363,86585,913390,661429,5651,953,30520,705,033103,525,165
-1-5-53-241-265-1,205-1,621-8,105-12,773-63,865-85,913-390,661-429,565-1,953,305-20,705,033-103,525,165

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