Q: What are the factor combinations of the number 4,600,345?

 A:
Positive:   1 x 46003455 x 92006923 x 200015109 x 42205115 x 40003367 x 12535545 x 84411835 x 2507
Negative: -1 x -4600345-5 x -920069-23 x -200015-109 x -42205-115 x -40003-367 x -12535-545 x -8441-1835 x -2507


How do I find the factor combinations of the number 4,600,345?

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 4,600,345, 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 4,600,345
-1 -4,600,345

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 4,600,345.

Example:
1 x 4,600,345 = 4,600,345
and
-1 x -4,600,345 = 4,600,345
Notice both answers equal 4,600,345

With that explanation out of the way, let's continue. Next, we take the number 4,600,345 and divide it by 2:

4,600,345 ÷ 2 = 2,300,172.5

If the quotient is a whole number, then 2 and 2,300,172.5 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 4,600,345
-1 -4,600,345

Now, we try dividing 4,600,345 by 3:

4,600,345 ÷ 3 = 1,533,448.3333

If the quotient is a whole number, then 3 and 1,533,448.3333 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 4,600,345
-1 -4,600,345

Let's try dividing by 4:

4,600,345 ÷ 4 = 1,150,086.25

If the quotient is a whole number, then 4 and 1,150,086.25 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 4,600,345
-1 4,600,345
Keep dividing by the next highest number until you cannot divide anymore.

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

15231091153675451,8352,5078,44112,53540,00342,205200,015920,0694,600,345
-1-5-23-109-115-367-545-1,835-2,507-8,441-12,535-40,003-42,205-200,015-920,069-4,600,345

More Examples

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