Q: What are the factor combinations of the number 421,322,004?

 A:
Positive:   1 x 4213220042 x 2106610023 x 1404406684 x 1053305016 x 702203349 x 4681355612 x 3511016718 x 2340677823 x 1831834836 x 1170338946 x 915917469 x 610611692 x 4579587138 x 3053058199 x 2117196207 x 2035372276 x 1526529398 x 1058598414 x 1017686597 x 705732796 x 529299828 x 5088431194 x 3528661791 x 2352442388 x 1764332557 x 1647723582 x 1176224577 x 920525114 x 823867164 x 588117671 x 549249154 x 4602610228 x 4119313731 x 3068415342 x 2746218308 x 23013
Negative: -1 x -421322004-2 x -210661002-3 x -140440668-4 x -105330501-6 x -70220334-9 x -46813556-12 x -35110167-18 x -23406778-23 x -18318348-36 x -11703389-46 x -9159174-69 x -6106116-92 x -4579587-138 x -3053058-199 x -2117196-207 x -2035372-276 x -1526529-398 x -1058598-414 x -1017686-597 x -705732-796 x -529299-828 x -508843-1194 x -352866-1791 x -235244-2388 x -176433-2557 x -164772-3582 x -117622-4577 x -92052-5114 x -82386-7164 x -58811-7671 x -54924-9154 x -46026-10228 x -41193-13731 x -30684-15342 x -27462-18308 x -23013


How do I find the factor combinations of the number 421,322,004?

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 421,322,004, 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.

1 421,322,004
-1 -421,322,004

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 421,322,004.

Example:
1 x 421,322,004 = 421,322,004
and
-1 x -421,322,004 = 421,322,004
Notice both answers equal 421,322,004

With that explanation out of the way, let's continue. Next, we take the number 421,322,004 and divide it by 2:

421,322,004 ÷ 2 = 210,661,002

If the quotient is a whole number, then 2 and 210,661,002 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 2 210,661,002 421,322,004
-1 -2 -210,661,002 -421,322,004

Now, we try dividing 421,322,004 by 3:

421,322,004 ÷ 3 = 140,440,668

If the quotient is a whole number, then 3 and 140,440,668 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 3 140,440,668 210,661,002 421,322,004
-1 -2 -3 -140,440,668 -210,661,002 -421,322,004

Let's try dividing by 4:

421,322,004 ÷ 4 = 105,330,501

If the quotient is a whole number, then 4 and 105,330,501 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 4 105,330,501 140,440,668 210,661,002 421,322,004
-1 -2 -3 -4 -105,330,501 -140,440,668 -210,661,002 421,322,004
Keep dividing by the next highest number until you cannot divide anymore.

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

123469121823364669921381992072763984145977968281,1941,7912,3882,5573,5824,5775,1147,1647,6719,15410,22813,73115,34218,30823,01327,46230,68441,19346,02654,92458,81182,38692,052117,622164,772176,433235,244352,866508,843529,299705,7321,017,6861,058,5981,526,5292,035,3722,117,1963,053,0584,579,5876,106,1169,159,17411,703,38918,318,34823,406,77835,110,16746,813,55670,220,334105,330,501140,440,668210,661,002421,322,004
-1-2-3-4-6-9-12-18-23-36-46-69-92-138-199-207-276-398-414-597-796-828-1,194-1,791-2,388-2,557-3,582-4,577-5,114-7,164-7,671-9,154-10,228-13,731-15,342-18,308-23,013-27,462-30,684-41,193-46,026-54,924-58,811-82,386-92,052-117,622-164,772-176,433-235,244-352,866-508,843-529,299-705,732-1,017,686-1,058,598-1,526,529-2,035,372-2,117,196-3,053,058-4,579,587-6,106,116-9,159,174-11,703,389-18,318,348-23,406,778-35,110,167-46,813,556-70,220,334-105,330,501-140,440,668-210,661,002-421,322,004

More Examples

Here are some more numbers to try:

421,322,002421,322,003421,322,005421,322,006
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