Q: What are the factor combinations of the number 42,301,325?

 A:
Positive:   1 x 423013255 x 846026511 x 384557525 x 169205355 x 769115101 x 418825275 x 153823505 x 837651111 x 380751523 x 277752525 x 167535555 x 7615
Negative: -1 x -42301325-5 x -8460265-11 x -3845575-25 x -1692053-55 x -769115-101 x -418825-275 x -153823-505 x -83765-1111 x -38075-1523 x -27775-2525 x -16753-5555 x -7615


How do I find the factor combinations of the number 42,301,325?

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 42,301,325, 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 42,301,325
-1 -42,301,325

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 42,301,325.

Example:
1 x 42,301,325 = 42,301,325
and
-1 x -42,301,325 = 42,301,325
Notice both answers equal 42,301,325

With that explanation out of the way, let's continue. Next, we take the number 42,301,325 and divide it by 2:

42,301,325 ÷ 2 = 21,150,662.5

If the quotient is a whole number, then 2 and 21,150,662.5 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 42,301,325
-1 -42,301,325

Now, we try dividing 42,301,325 by 3:

42,301,325 ÷ 3 = 14,100,441.6667

If the quotient is a whole number, then 3 and 14,100,441.6667 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 42,301,325
-1 -42,301,325

Let's try dividing by 4:

42,301,325 ÷ 4 = 10,575,331.25

If the quotient is a whole number, then 4 and 10,575,331.25 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 42,301,325
-1 42,301,325
Keep dividing by the next highest number until you cannot divide anymore.

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

151125551012755051,1111,5232,5255,5557,61516,75327,77538,07583,765153,823418,825769,1151,692,0533,845,5758,460,26542,301,325
-1-5-11-25-55-101-275-505-1,111-1,523-2,525-5,555-7,615-16,753-27,775-38,075-83,765-153,823-418,825-769,115-1,692,053-3,845,575-8,460,265-42,301,325

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