Q: What are the factor combinations of the number 42,542,305?

 A:
Positive:   1 x 425423055 x 850846113 x 327248553 x 80268565 x 654497233 x 182585265 x 160537689 x 617451165 x 365172809 x 151453029 x 140453445 x 12349
Negative: -1 x -42542305-5 x -8508461-13 x -3272485-53 x -802685-65 x -654497-233 x -182585-265 x -160537-689 x -61745-1165 x -36517-2809 x -15145-3029 x -14045-3445 x -12349


How do I find the factor combinations of the number 42,542,305?

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 42,542,305, 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 42,542,305
-1 -42,542,305

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 42,542,305.

Example:
1 x 42,542,305 = 42,542,305
and
-1 x -42,542,305 = 42,542,305
Notice both answers equal 42,542,305

With that explanation out of the way, let's continue. Next, we take the number 42,542,305 and divide it by 2:

42,542,305 ÷ 2 = 21,271,152.5

If the quotient is a whole number, then 2 and 21,271,152.5 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 42,542,305
-1 -42,542,305

Now, we try dividing 42,542,305 by 3:

42,542,305 ÷ 3 = 14,180,768.3333

If the quotient is a whole number, then 3 and 14,180,768.3333 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 42,542,305
-1 -42,542,305

Let's try dividing by 4:

42,542,305 ÷ 4 = 10,635,576.25

If the quotient is a whole number, then 4 and 10,635,576.25 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 42,542,305
-1 42,542,305
Keep dividing by the next highest number until you cannot divide anymore.

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

151353652332656891,1652,8093,0293,44512,34914,04515,14536,51761,745160,537182,585654,497802,6853,272,4858,508,46142,542,305
-1-5-13-53-65-233-265-689-1,165-2,809-3,029-3,445-12,349-14,045-15,145-36,517-61,745-160,537-182,585-654,497-802,685-3,272,485-8,508,461-42,542,305

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