Q: What are the factor combinations of the number 146,545,013?

 A:
Positive:   1 x 14654501347 x 311797967 x 2187239173 x 847081269 x 5447773149 x 465378131 x 1802311591 x 12643
Negative: -1 x -146545013-47 x -3117979-67 x -2187239-173 x -847081-269 x -544777-3149 x -46537-8131 x -18023-11591 x -12643


How do I find the factor combinations of the number 146,545,013?

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 146,545,013, 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.

1 146,545,013
-1 -146,545,013

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 146,545,013.

Example:
1 x 146,545,013 = 146,545,013
and
-1 x -146,545,013 = 146,545,013
Notice both answers equal 146,545,013

With that explanation out of the way, let's continue. Next, we take the number 146,545,013 and divide it by 2:

146,545,013 ÷ 2 = 73,272,506.5

If the quotient is a whole number, then 2 and 73,272,506.5 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:

1 146,545,013
-1 -146,545,013

Now, we try dividing 146,545,013 by 3:

146,545,013 ÷ 3 = 48,848,337.6667

If the quotient is a whole number, then 3 and 48,848,337.6667 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:

1 146,545,013
-1 -146,545,013

Let's try dividing by 4:

146,545,013 ÷ 4 = 36,636,253.25

If the quotient is a whole number, then 4 and 36,636,253.25 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:

1 146,545,013
-1 146,545,013
Keep dividing by the next highest number until you cannot divide anymore.

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

147671732693,1498,13111,59112,64318,02346,537544,777847,0812,187,2393,117,979146,545,013
-1-47-67-173-269-3,149-8,131-11,591-12,643-18,023-46,537-544,777-847,081-2,187,239-3,117,979-146,545,013

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