Q: What are the factor combinations of the number 150,420,029?

 A:
Positive:   1 x 15042002917 x 884823731 x 485225979 x 1904051527 x 2854271343 x 1120032449 x 614213613 x 41633
Negative: -1 x -150420029-17 x -8848237-31 x -4852259-79 x -1904051-527 x -285427-1343 x -112003-2449 x -61421-3613 x -41633


How do I find the factor combinations of the number 150,420,029?

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 150,420,029, 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.

1 150,420,029
-1 -150,420,029

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 150,420,029.

Example:
1 x 150,420,029 = 150,420,029
and
-1 x -150,420,029 = 150,420,029
Notice both answers equal 150,420,029

With that explanation out of the way, let's continue. Next, we take the number 150,420,029 and divide it by 2:

150,420,029 ÷ 2 = 75,210,014.5

If the quotient is a whole number, then 2 and 75,210,014.5 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:

1 150,420,029
-1 -150,420,029

Now, we try dividing 150,420,029 by 3:

150,420,029 ÷ 3 = 50,140,009.6667

If the quotient is a whole number, then 3 and 50,140,009.6667 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:

1 150,420,029
-1 -150,420,029

Let's try dividing by 4:

150,420,029 ÷ 4 = 37,605,007.25

If the quotient is a whole number, then 4 and 37,605,007.25 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:

1 150,420,029
-1 150,420,029
Keep dividing by the next highest number until you cannot divide anymore.

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

11731795271,3432,4493,61341,63361,421112,003285,4271,904,0514,852,2598,848,237150,420,029
-1-17-31-79-527-1,343-2,449-3,613-41,633-61,421-112,003-285,427-1,904,051-4,852,259-8,848,237-150,420,029

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