Q: What are the factor combinations of the number 42,123,025?

 A:
Positive:   1 x 421230255 x 84246057 x 601757517 x 247782525 x 168492135 x 120351585 x 495565119 x 353975175 x 240703425 x 99113595 x 707952975 x 14159
Negative: -1 x -42123025-5 x -8424605-7 x -6017575-17 x -2477825-25 x -1684921-35 x -1203515-85 x -495565-119 x -353975-175 x -240703-425 x -99113-595 x -70795-2975 x -14159


How do I find the factor combinations of the number 42,123,025?

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 42,123,025, 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 42,123,025
-1 -42,123,025

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 42,123,025.

Example:
1 x 42,123,025 = 42,123,025
and
-1 x -42,123,025 = 42,123,025
Notice both answers equal 42,123,025

With that explanation out of the way, let's continue. Next, we take the number 42,123,025 and divide it by 2:

42,123,025 ÷ 2 = 21,061,512.5

If the quotient is a whole number, then 2 and 21,061,512.5 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 42,123,025
-1 -42,123,025

Now, we try dividing 42,123,025 by 3:

42,123,025 ÷ 3 = 14,041,008.3333

If the quotient is a whole number, then 3 and 14,041,008.3333 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 42,123,025
-1 -42,123,025

Let's try dividing by 4:

42,123,025 ÷ 4 = 10,530,756.25

If the quotient is a whole number, then 4 and 10,530,756.25 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 42,123,025
-1 42,123,025
Keep dividing by the next highest number until you cannot divide anymore.

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

157172535851191754255952,97514,15970,79599,113240,703353,975495,5651,203,5151,684,9212,477,8256,017,5758,424,60542,123,025
-1-5-7-17-25-35-85-119-175-425-595-2,975-14,159-70,795-99,113-240,703-353,975-495,565-1,203,515-1,684,921-2,477,825-6,017,575-8,424,605-42,123,025

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