Q: What are the factor combinations of the number 123,106,104?

 A:
Positive:   1 x 1231061042 x 615530523 x 410353684 x 307765266 x 205176848 x 153882639 x 1367845611 x 1119146412 x 1025884218 x 683922822 x 559573224 x 512942133 x 373048836 x 341961437 x 332719244 x 279786666 x 186524472 x 170980774 x 166359688 x 139893399 x 1243496111 x 1109064132 x 932622148 x 831798198 x 621748222 x 554532264 x 466311296 x 415899333 x 369688396 x 310874407 x 302472444 x 277266666 x 184844792 x 155437814 x 151236888 x 1386331221 x 1008241332 x 924221628 x 756182442 x 504122664 x 462113256 x 378093663 x 336084201 x 293044884 x 252067326 x 168048402 x 146529768 x 12603
Negative: -1 x -123106104-2 x -61553052-3 x -41035368-4 x -30776526-6 x -20517684-8 x -15388263-9 x -13678456-11 x -11191464-12 x -10258842-18 x -6839228-22 x -5595732-24 x -5129421-33 x -3730488-36 x -3419614-37 x -3327192-44 x -2797866-66 x -1865244-72 x -1709807-74 x -1663596-88 x -1398933-99 x -1243496-111 x -1109064-132 x -932622-148 x -831798-198 x -621748-222 x -554532-264 x -466311-296 x -415899-333 x -369688-396 x -310874-407 x -302472-444 x -277266-666 x -184844-792 x -155437-814 x -151236-888 x -138633-1221 x -100824-1332 x -92422-1628 x -75618-2442 x -50412-2664 x -46211-3256 x -37809-3663 x -33608-4201 x -29304-4884 x -25206-7326 x -16804-8402 x -14652-9768 x -12603


How do I find the factor combinations of the number 123,106,104?

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 123,106,104, 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.

1 123,106,104
-1 -123,106,104

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 123,106,104.

Example:
1 x 123,106,104 = 123,106,104
and
-1 x -123,106,104 = 123,106,104
Notice both answers equal 123,106,104

With that explanation out of the way, let's continue. Next, we take the number 123,106,104 and divide it by 2:

123,106,104 ÷ 2 = 61,553,052

If the quotient is a whole number, then 2 and 61,553,052 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 61,553,052 123,106,104
-1 -2 -61,553,052 -123,106,104

Now, we try dividing 123,106,104 by 3:

123,106,104 ÷ 3 = 41,035,368

If the quotient is a whole number, then 3 and 41,035,368 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 41,035,368 61,553,052 123,106,104
-1 -2 -3 -41,035,368 -61,553,052 -123,106,104

Let's try dividing by 4:

123,106,104 ÷ 4 = 30,776,526

If the quotient is a whole number, then 4 and 30,776,526 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 30,776,526 41,035,368 61,553,052 123,106,104
-1 -2 -3 -4 -30,776,526 -41,035,368 -61,553,052 123,106,104
Keep dividing by the next highest number until you cannot divide anymore.

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

123468911121822243336374466727488991111321481982222642963333964074446667928148881,2211,3321,6282,4422,6643,2563,6634,2014,8847,3268,4029,76812,60314,65216,80425,20629,30433,60837,80946,21150,41275,61892,422100,824138,633151,236155,437184,844277,266302,472310,874369,688415,899466,311554,532621,748831,798932,6221,109,0641,243,4961,398,9331,663,5961,709,8071,865,2442,797,8663,327,1923,419,6143,730,4885,129,4215,595,7326,839,22810,258,84211,191,46413,678,45615,388,26320,517,68430,776,52641,035,36861,553,052123,106,104
-1-2-3-4-6-8-9-11-12-18-22-24-33-36-37-44-66-72-74-88-99-111-132-148-198-222-264-296-333-396-407-444-666-792-814-888-1,221-1,332-1,628-2,442-2,664-3,256-3,663-4,201-4,884-7,326-8,402-9,768-12,603-14,652-16,804-25,206-29,304-33,608-37,809-46,211-50,412-75,618-92,422-100,824-138,633-151,236-155,437-184,844-277,266-302,472-310,874-369,688-415,899-466,311-554,532-621,748-831,798-932,622-1,109,064-1,243,496-1,398,933-1,663,596-1,709,807-1,865,244-2,797,866-3,327,192-3,419,614-3,730,488-5,129,421-5,595,732-6,839,228-10,258,842-11,191,464-13,678,456-15,388,263-20,517,684-30,776,526-41,035,368-61,553,052-123,106,104

More Examples

Here are some more numbers to try:

123,106,102123,106,103123,106,105123,106,106
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