Q: What are the factor combinations of the number 104,121,144?

 A:
Positive:   1 x 1041211442 x 520605723 x 347070484 x 260302866 x 173535248 x 130151439 x 1156901612 x 867676218 x 578450824 x 433838136 x 289225461 x 170690472 x 1446127122 x 853452151 x 689544157 x 663192183 x 568968244 x 426726302 x 344772314 x 331596366 x 284484453 x 229848471 x 221064488 x 213363549 x 189656604 x 172386628 x 165798732 x 142242906 x 114924942 x 1105321098 x 948281208 x 861931256 x 828991359 x 766161413 x 736881464 x 711211812 x 574621884 x 552662196 x 474142718 x 383082826 x 368443624 x 287313768 x 276334392 x 237075436 x 191545652 x 184229211 x 113049577 x 10872
Negative: -1 x -104121144-2 x -52060572-3 x -34707048-4 x -26030286-6 x -17353524-8 x -13015143-9 x -11569016-12 x -8676762-18 x -5784508-24 x -4338381-36 x -2892254-61 x -1706904-72 x -1446127-122 x -853452-151 x -689544-157 x -663192-183 x -568968-244 x -426726-302 x -344772-314 x -331596-366 x -284484-453 x -229848-471 x -221064-488 x -213363-549 x -189656-604 x -172386-628 x -165798-732 x -142242-906 x -114924-942 x -110532-1098 x -94828-1208 x -86193-1256 x -82899-1359 x -76616-1413 x -73688-1464 x -71121-1812 x -57462-1884 x -55266-2196 x -47414-2718 x -38308-2826 x -36844-3624 x -28731-3768 x -27633-4392 x -23707-5436 x -19154-5652 x -18422-9211 x -11304-9577 x -10872


How do I find the factor combinations of the number 104,121,144?

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 104,121,144, 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.

1 104,121,144
-1 -104,121,144

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 104,121,144.

Example:
1 x 104,121,144 = 104,121,144
and
-1 x -104,121,144 = 104,121,144
Notice both answers equal 104,121,144

With that explanation out of the way, let's continue. Next, we take the number 104,121,144 and divide it by 2:

104,121,144 ÷ 2 = 52,060,572

If the quotient is a whole number, then 2 and 52,060,572 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 52,060,572 104,121,144
-1 -2 -52,060,572 -104,121,144

Now, we try dividing 104,121,144 by 3:

104,121,144 ÷ 3 = 34,707,048

If the quotient is a whole number, then 3 and 34,707,048 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 34,707,048 52,060,572 104,121,144
-1 -2 -3 -34,707,048 -52,060,572 -104,121,144

Let's try dividing by 4:

104,121,144 ÷ 4 = 26,030,286

If the quotient is a whole number, then 4 and 26,030,286 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 26,030,286 34,707,048 52,060,572 104,121,144
-1 -2 -3 -4 -26,030,286 -34,707,048 -52,060,572 104,121,144
Keep dividing by the next highest number until you cannot divide anymore.

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

12346891218243661721221511571832443023143664534714885496046287329069421,0981,2081,2561,3591,4131,4641,8121,8842,1962,7182,8263,6243,7684,3925,4365,6529,2119,57710,87211,30418,42219,15423,70727,63328,73136,84438,30847,41455,26657,46271,12173,68876,61682,89986,19394,828110,532114,924142,242165,798172,386189,656213,363221,064229,848284,484331,596344,772426,726568,968663,192689,544853,4521,446,1271,706,9042,892,2544,338,3815,784,5088,676,76211,569,01613,015,14317,353,52426,030,28634,707,04852,060,572104,121,144
-1-2-3-4-6-8-9-12-18-24-36-61-72-122-151-157-183-244-302-314-366-453-471-488-549-604-628-732-906-942-1,098-1,208-1,256-1,359-1,413-1,464-1,812-1,884-2,196-2,718-2,826-3,624-3,768-4,392-5,436-5,652-9,211-9,577-10,872-11,304-18,422-19,154-23,707-27,633-28,731-36,844-38,308-47,414-55,266-57,462-71,121-73,688-76,616-82,899-86,193-94,828-110,532-114,924-142,242-165,798-172,386-189,656-213,363-221,064-229,848-284,484-331,596-344,772-426,726-568,968-663,192-689,544-853,452-1,446,127-1,706,904-2,892,254-4,338,381-5,784,508-8,676,762-11,569,016-13,015,143-17,353,524-26,030,286-34,707,048-52,060,572-104,121,144

More Examples

Here are some more numbers to try:

104,121,142104,121,143104,121,145104,121,146
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