Q: What are the factor combinations of the number 103,142,053?

 A:
Positive:   1 x 1031420537 x 1473457931 x 3327163217 x 475309421 x 2449931129 x 913572947 x 349997903 x 13051
Negative: -1 x -103142053-7 x -14734579-31 x -3327163-217 x -475309-421 x -244993-1129 x -91357-2947 x -34999-7903 x -13051


How do I find the factor combinations of the number 103,142,053?

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 103,142,053, 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.

1 103,142,053
-1 -103,142,053

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 103,142,053.

Example:
1 x 103,142,053 = 103,142,053
and
-1 x -103,142,053 = 103,142,053
Notice both answers equal 103,142,053

With that explanation out of the way, let's continue. Next, we take the number 103,142,053 and divide it by 2:

103,142,053 ÷ 2 = 51,571,026.5

If the quotient is a whole number, then 2 and 51,571,026.5 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:

1 103,142,053
-1 -103,142,053

Now, we try dividing 103,142,053 by 3:

103,142,053 ÷ 3 = 34,380,684.3333

If the quotient is a whole number, then 3 and 34,380,684.3333 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:

1 103,142,053
-1 -103,142,053

Let's try dividing by 4:

103,142,053 ÷ 4 = 25,785,513.25

If the quotient is a whole number, then 4 and 25,785,513.25 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:

1 103,142,053
-1 103,142,053
Keep dividing by the next highest number until you cannot divide anymore.

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

17312174211,1292,9477,90313,05134,99991,357244,993475,3093,327,16314,734,579103,142,053
-1-7-31-217-421-1,129-2,947-7,903-13,051-34,999-91,357-244,993-475,309-3,327,163-14,734,579-103,142,053

More Examples

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