Q: What are the factor combinations of the number 48,106,723?

 A:
Positive:   1 x 481067237 x 687238943 x 1118761181 x 265783301 x 159823883 x 544811267 x 379696181 x 7783
Negative: -1 x -48106723-7 x -6872389-43 x -1118761-181 x -265783-301 x -159823-883 x -54481-1267 x -37969-6181 x -7783


How do I find the factor combinations of the number 48,106,723?

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 48,106,723, 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 48,106,723
-1 -48,106,723

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 48,106,723.

Example:
1 x 48,106,723 = 48,106,723
and
-1 x -48,106,723 = 48,106,723
Notice both answers equal 48,106,723

With that explanation out of the way, let's continue. Next, we take the number 48,106,723 and divide it by 2:

48,106,723 ÷ 2 = 24,053,361.5

If the quotient is a whole number, then 2 and 24,053,361.5 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 48,106,723
-1 -48,106,723

Now, we try dividing 48,106,723 by 3:

48,106,723 ÷ 3 = 16,035,574.3333

If the quotient is a whole number, then 3 and 16,035,574.3333 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 48,106,723
-1 -48,106,723

Let's try dividing by 4:

48,106,723 ÷ 4 = 12,026,680.75

If the quotient is a whole number, then 4 and 12,026,680.75 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 48,106,723
-1 48,106,723
Keep dividing by the next highest number until you cannot divide anymore.

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

17431813018831,2676,1817,78337,96954,481159,823265,7831,118,7616,872,38948,106,723
-1-7-43-181-301-883-1,267-6,181-7,783-37,969-54,481-159,823-265,783-1,118,761-6,872,389-48,106,723

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