Q: What are the factor combinations of the number 103,432,021?

 A:
Positive:   1 x 1034320217 x 1477600311 x 940291173 x 141687777 x 1343273511 x 202411803 x 1288075621 x 18401
Negative: -1 x -103432021-7 x -14776003-11 x -9402911-73 x -1416877-77 x -1343273-511 x -202411-803 x -128807-5621 x -18401


How do I find the factor combinations of the number 103,432,021?

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 103,432,021, 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.

1 103,432,021
-1 -103,432,021

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 103,432,021.

Example:
1 x 103,432,021 = 103,432,021
and
-1 x -103,432,021 = 103,432,021
Notice both answers equal 103,432,021

With that explanation out of the way, let's continue. Next, we take the number 103,432,021 and divide it by 2:

103,432,021 ÷ 2 = 51,716,010.5

If the quotient is a whole number, then 2 and 51,716,010.5 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:

1 103,432,021
-1 -103,432,021

Now, we try dividing 103,432,021 by 3:

103,432,021 ÷ 3 = 34,477,340.3333

If the quotient is a whole number, then 3 and 34,477,340.3333 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:

1 103,432,021
-1 -103,432,021

Let's try dividing by 4:

103,432,021 ÷ 4 = 25,858,005.25

If the quotient is a whole number, then 4 and 25,858,005.25 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:

1 103,432,021
-1 103,432,021
Keep dividing by the next highest number until you cannot divide anymore.

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

171173775118035,62118,401128,807202,4111,343,2731,416,8779,402,91114,776,003103,432,021
-1-7-11-73-77-511-803-5,621-18,401-128,807-202,411-1,343,273-1,416,877-9,402,911-14,776,003-103,432,021

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