Q: What are the factor combinations of the number 146,234,621?

 A:
Positive:   1 x 14623462113 x 1124881719 x 769655923 x 6358027247 x 592043299 x 489079437 x 3346335681 x 25741
Negative: -1 x -146234621-13 x -11248817-19 x -7696559-23 x -6358027-247 x -592043-299 x -489079-437 x -334633-5681 x -25741


How do I find the factor combinations of the number 146,234,621?

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 146,234,621, 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.

1 146,234,621
-1 -146,234,621

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 146,234,621.

Example:
1 x 146,234,621 = 146,234,621
and
-1 x -146,234,621 = 146,234,621
Notice both answers equal 146,234,621

With that explanation out of the way, let's continue. Next, we take the number 146,234,621 and divide it by 2:

146,234,621 ÷ 2 = 73,117,310.5

If the quotient is a whole number, then 2 and 73,117,310.5 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:

1 146,234,621
-1 -146,234,621

Now, we try dividing 146,234,621 by 3:

146,234,621 ÷ 3 = 48,744,873.6667

If the quotient is a whole number, then 3 and 48,744,873.6667 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:

1 146,234,621
-1 -146,234,621

Let's try dividing by 4:

146,234,621 ÷ 4 = 36,558,655.25

If the quotient is a whole number, then 4 and 36,558,655.25 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:

1 146,234,621
-1 146,234,621
Keep dividing by the next highest number until you cannot divide anymore.

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

11319232472994375,68125,741334,633489,079592,0436,358,0277,696,55911,248,817146,234,621
-1-13-19-23-247-299-437-5,681-25,741-334,633-489,079-592,043-6,358,027-7,696,559-11,248,817-146,234,621

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