Q: What are the factor combinations of the number 13,742,105?

 A:
Positive:   1 x 137421055 x 274842113 x 105708553 x 25928565 x 211417265 x 51857689 x 199453445 x 3989
Negative: -1 x -13742105-5 x -2748421-13 x -1057085-53 x -259285-65 x -211417-265 x -51857-689 x -19945-3445 x -3989


How do I find the factor combinations of the number 13,742,105?

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 13,742,105, 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 13,742,105
-1 -13,742,105

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 13,742,105.

Example:
1 x 13,742,105 = 13,742,105
and
-1 x -13,742,105 = 13,742,105
Notice both answers equal 13,742,105

With that explanation out of the way, let's continue. Next, we take the number 13,742,105 and divide it by 2:

13,742,105 ÷ 2 = 6,871,052.5

If the quotient is a whole number, then 2 and 6,871,052.5 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 13,742,105
-1 -13,742,105

Now, we try dividing 13,742,105 by 3:

13,742,105 ÷ 3 = 4,580,701.6667

If the quotient is a whole number, then 3 and 4,580,701.6667 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 13,742,105
-1 -13,742,105

Let's try dividing by 4:

13,742,105 ÷ 4 = 3,435,526.25

If the quotient is a whole number, then 4 and 3,435,526.25 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 13,742,105
-1 13,742,105
Keep dividing by the next highest number until you cannot divide anymore.

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

151353652656893,4453,98919,94551,857211,417259,2851,057,0852,748,42113,742,105
-1-5-13-53-65-265-689-3,445-3,989-19,945-51,857-211,417-259,285-1,057,085-2,748,421-13,742,105

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