Q: What are the factor combinations of the number 46,416,125?

 A:
Positive:   1 x 464161255 x 92832257 x 663087525 x 185664535 x 1326175125 x 371329175 x 265235875 x 53047
Negative: -1 x -46416125-5 x -9283225-7 x -6630875-25 x -1856645-35 x -1326175-125 x -371329-175 x -265235-875 x -53047


How do I find the factor combinations of the number 46,416,125?

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 46,416,125, 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 46,416,125
-1 -46,416,125

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 46,416,125.

Example:
1 x 46,416,125 = 46,416,125
and
-1 x -46,416,125 = 46,416,125
Notice both answers equal 46,416,125

With that explanation out of the way, let's continue. Next, we take the number 46,416,125 and divide it by 2:

46,416,125 ÷ 2 = 23,208,062.5

If the quotient is a whole number, then 2 and 23,208,062.5 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 46,416,125
-1 -46,416,125

Now, we try dividing 46,416,125 by 3:

46,416,125 ÷ 3 = 15,472,041.6667

If the quotient is a whole number, then 3 and 15,472,041.6667 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 46,416,125
-1 -46,416,125

Let's try dividing by 4:

46,416,125 ÷ 4 = 11,604,031.25

If the quotient is a whole number, then 4 and 11,604,031.25 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 46,416,125
-1 46,416,125
Keep dividing by the next highest number until you cannot divide anymore.

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

157253512517587553,047265,235371,3291,326,1751,856,6456,630,8759,283,22546,416,125
-1-5-7-25-35-125-175-875-53,047-265,235-371,329-1,326,175-1,856,645-6,630,875-9,283,225-46,416,125

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