Q: What are the factor combinations of the number 103,025,429?

 A:
Positive:   1 x 10302542913 x 792503319 x 542239129 x 3552601247 x 417107361 x 285389377 x 273277551 x 186979757 x 1360974693 x 219537163 x 143839841 x 10469
Negative: -1 x -103025429-13 x -7925033-19 x -5422391-29 x -3552601-247 x -417107-361 x -285389-377 x -273277-551 x -186979-757 x -136097-4693 x -21953-7163 x -14383-9841 x -10469


How do I find the factor combinations of the number 103,025,429?

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 103,025,429, 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.

1 103,025,429
-1 -103,025,429

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 103,025,429.

Example:
1 x 103,025,429 = 103,025,429
and
-1 x -103,025,429 = 103,025,429
Notice both answers equal 103,025,429

With that explanation out of the way, let's continue. Next, we take the number 103,025,429 and divide it by 2:

103,025,429 ÷ 2 = 51,512,714.5

If the quotient is a whole number, then 2 and 51,512,714.5 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:

1 103,025,429
-1 -103,025,429

Now, we try dividing 103,025,429 by 3:

103,025,429 ÷ 3 = 34,341,809.6667

If the quotient is a whole number, then 3 and 34,341,809.6667 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:

1 103,025,429
-1 -103,025,429

Let's try dividing by 4:

103,025,429 ÷ 4 = 25,756,357.25

If the quotient is a whole number, then 4 and 25,756,357.25 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:

1 103,025,429
-1 103,025,429
Keep dividing by the next highest number until you cannot divide anymore.

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

11319292473613775517574,6937,1639,84110,46914,38321,953136,097186,979273,277285,389417,1073,552,6015,422,3917,925,033103,025,429
-1-13-19-29-247-361-377-551-757-4,693-7,163-9,841-10,469-14,383-21,953-136,097-186,979-273,277-285,389-417,107-3,552,601-5,422,391-7,925,033-103,025,429

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