Q: What are the factor combinations of the number 210,231,420?

 A:
Positive:   1 x 2102314202 x 1051157103 x 700771404 x 525578555 x 420462846 x 350385707 x 3003306010 x 2102314212 x 1751928514 x 1501653015 x 1401542820 x 1051157121 x 1001102028 x 750826530 x 700771435 x 600661242 x 500551060 x 350385770 x 300330684 x 2502755105 x 2002204131 x 1604820140 x 1501653210 x 1001102262 x 802410393 x 534940420 x 500551524 x 401205655 x 320964786 x 267470917 x 2292601310 x 1604821572 x 1337351834 x 1146301965 x 1069882620 x 802412751 x 764203668 x 573153821 x 550203930 x 534944585 x 458525502 x 382107642 x 275107860 x 267479170 x 2292611004 x 1910511463 x 1834013755 x 15284
Negative: -1 x -210231420-2 x -105115710-3 x -70077140-4 x -52557855-5 x -42046284-6 x -35038570-7 x -30033060-10 x -21023142-12 x -17519285-14 x -15016530-15 x -14015428-20 x -10511571-21 x -10011020-28 x -7508265-30 x -7007714-35 x -6006612-42 x -5005510-60 x -3503857-70 x -3003306-84 x -2502755-105 x -2002204-131 x -1604820-140 x -1501653-210 x -1001102-262 x -802410-393 x -534940-420 x -500551-524 x -401205-655 x -320964-786 x -267470-917 x -229260-1310 x -160482-1572 x -133735-1834 x -114630-1965 x -106988-2620 x -80241-2751 x -76420-3668 x -57315-3821 x -55020-3930 x -53494-4585 x -45852-5502 x -38210-7642 x -27510-7860 x -26747-9170 x -22926-11004 x -19105-11463 x -18340-13755 x -15284


How do I find the factor combinations of the number 210,231,420?

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 210,231,420, 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.

1 210,231,420
-1 -210,231,420

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 210,231,420.

Example:
1 x 210,231,420 = 210,231,420
and
-1 x -210,231,420 = 210,231,420
Notice both answers equal 210,231,420

With that explanation out of the way, let's continue. Next, we take the number 210,231,420 and divide it by 2:

210,231,420 ÷ 2 = 105,115,710

If the quotient is a whole number, then 2 and 105,115,710 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 2 105,115,710 210,231,420
-1 -2 -105,115,710 -210,231,420

Now, we try dividing 210,231,420 by 3:

210,231,420 ÷ 3 = 70,077,140

If the quotient is a whole number, then 3 and 70,077,140 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 70,077,140 105,115,710 210,231,420
-1 -2 -3 -70,077,140 -105,115,710 -210,231,420

Let's try dividing by 4:

210,231,420 ÷ 4 = 52,557,855

If the quotient is a whole number, then 4 and 52,557,855 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 52,557,855 70,077,140 105,115,710 210,231,420
-1 -2 -3 -4 -52,557,855 -70,077,140 -105,115,710 210,231,420
Keep dividing by the next highest number until you cannot divide anymore.

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

1234567101214152021283035426070841051311402102623934205246557869171,3101,5721,8341,9652,6202,7513,6683,8213,9304,5855,5027,6427,8609,17011,00411,46313,75515,28418,34019,10522,92626,74727,51038,21045,85253,49455,02057,31576,42080,241106,988114,630133,735160,482229,260267,470320,964401,205500,551534,940802,4101,001,1021,501,6531,604,8202,002,2042,502,7553,003,3063,503,8575,005,5106,006,6127,007,7147,508,26510,011,02010,511,57114,015,42815,016,53017,519,28521,023,14230,033,06035,038,57042,046,28452,557,85570,077,140105,115,710210,231,420
-1-2-3-4-5-6-7-10-12-14-15-20-21-28-30-35-42-60-70-84-105-131-140-210-262-393-420-524-655-786-917-1,310-1,572-1,834-1,965-2,620-2,751-3,668-3,821-3,930-4,585-5,502-7,642-7,860-9,170-11,004-11,463-13,755-15,284-18,340-19,105-22,926-26,747-27,510-38,210-45,852-53,494-55,020-57,315-76,420-80,241-106,988-114,630-133,735-160,482-229,260-267,470-320,964-401,205-500,551-534,940-802,410-1,001,102-1,501,653-1,604,820-2,002,204-2,502,755-3,003,306-3,503,857-5,005,510-6,006,612-7,007,714-7,508,265-10,011,020-10,511,571-14,015,428-15,016,530-17,519,285-21,023,142-30,033,060-35,038,570-42,046,284-52,557,855-70,077,140-105,115,710-210,231,420

More Examples

Here are some more numbers to try:

210,231,418210,231,419210,231,421210,231,422
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