Q: What are the factor combinations of the number 24,135,461?

 A:
Positive:   1 x 241354617 x 344792317 x 1419733119 x 202819127 x 190043889 x 271491597 x 151132159 x 11179
Negative: -1 x -24135461-7 x -3447923-17 x -1419733-119 x -202819-127 x -190043-889 x -27149-1597 x -15113-2159 x -11179


How do I find the factor combinations of the number 24,135,461?

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 24,135,461, 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 24,135,461
-1 -24,135,461

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 24,135,461.

Example:
1 x 24,135,461 = 24,135,461
and
-1 x -24,135,461 = 24,135,461
Notice both answers equal 24,135,461

With that explanation out of the way, let's continue. Next, we take the number 24,135,461 and divide it by 2:

24,135,461 ÷ 2 = 12,067,730.5

If the quotient is a whole number, then 2 and 12,067,730.5 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 24,135,461
-1 -24,135,461

Now, we try dividing 24,135,461 by 3:

24,135,461 ÷ 3 = 8,045,153.6667

If the quotient is a whole number, then 3 and 8,045,153.6667 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 24,135,461
-1 -24,135,461

Let's try dividing by 4:

24,135,461 ÷ 4 = 6,033,865.25

If the quotient is a whole number, then 4 and 6,033,865.25 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 24,135,461
-1 24,135,461
Keep dividing by the next highest number until you cannot divide anymore.

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

17171191278891,5972,15911,17915,11327,149190,043202,8191,419,7333,447,92324,135,461
-1-7-17-119-127-889-1,597-2,159-11,179-15,113-27,149-190,043-202,819-1,419,733-3,447,923-24,135,461

More Examples

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