Q: What are the factor combinations of the number 304,144,260?

 A:
Positive:   1 x 3041442602 x 1520721303 x 1013814204 x 760360655 x 608288526 x 506907107 x 4344918010 x 3041442612 x 2534535514 x 2172459015 x 2027628420 x 1520721321 x 1448306028 x 1086229530 x 1013814235 x 868983642 x 724153060 x 506907170 x 434491884 x 3620765105 x 2896612140 x 2172459210 x 1448306420 x 724153
Negative: -1 x -304144260-2 x -152072130-3 x -101381420-4 x -76036065-5 x -60828852-6 x -50690710-7 x -43449180-10 x -30414426-12 x -25345355-14 x -21724590-15 x -20276284-20 x -15207213-21 x -14483060-28 x -10862295-30 x -10138142-35 x -8689836-42 x -7241530-60 x -5069071-70 x -4344918-84 x -3620765-105 x -2896612-140 x -2172459-210 x -1448306-420 x -724153


How do I find the factor combinations of the number 304,144,260?

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 304,144,260, 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.

1 304,144,260
-1 -304,144,260

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 304,144,260.

Example:
1 x 304,144,260 = 304,144,260
and
-1 x -304,144,260 = 304,144,260
Notice both answers equal 304,144,260

With that explanation out of the way, let's continue. Next, we take the number 304,144,260 and divide it by 2:

304,144,260 ÷ 2 = 152,072,130

If the quotient is a whole number, then 2 and 152,072,130 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 152,072,130 304,144,260
-1 -2 -152,072,130 -304,144,260

Now, we try dividing 304,144,260 by 3:

304,144,260 ÷ 3 = 101,381,420

If the quotient is a whole number, then 3 and 101,381,420 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 101,381,420 152,072,130 304,144,260
-1 -2 -3 -101,381,420 -152,072,130 -304,144,260

Let's try dividing by 4:

304,144,260 ÷ 4 = 76,036,065

If the quotient is a whole number, then 4 and 76,036,065 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 76,036,065 101,381,420 152,072,130 304,144,260
-1 -2 -3 -4 -76,036,065 -101,381,420 -152,072,130 304,144,260
Keep dividing by the next highest number until you cannot divide anymore.

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

123456710121415202128303542607084105140210420724,1531,448,3062,172,4592,896,6123,620,7654,344,9185,069,0717,241,5308,689,83610,138,14210,862,29514,483,06015,207,21320,276,28421,724,59025,345,35530,414,42643,449,18050,690,71060,828,85276,036,065101,381,420152,072,130304,144,260
-1-2-3-4-5-6-7-10-12-14-15-20-21-28-30-35-42-60-70-84-105-140-210-420-724,153-1,448,306-2,172,459-2,896,612-3,620,765-4,344,918-5,069,071-7,241,530-8,689,836-10,138,142-10,862,295-14,483,060-15,207,213-20,276,284-21,724,590-25,345,355-30,414,426-43,449,180-50,690,710-60,828,852-76,036,065-101,381,420-152,072,130-304,144,260

More Examples

Here are some more numbers to try:

304,144,258304,144,259304,144,261304,144,262
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