Q: What are the factor combinations of the number 401,102,304?

 A:
Positive:   1 x 4011023042 x 2005511523 x 1337007684 x 1002755766 x 668503848 x 5013778812 x 3342519216 x 2506889424 x 1671259631 x 1293878432 x 1253444748 x 835629853 x 756796862 x 646939293 x 431292896 x 4178149106 x 3783984124 x 3234696159 x 2522656186 x 2156464212 x 1891992248 x 1617348318 x 1261328372 x 1078232424 x 945996496 x 808674636 x 630664744 x 539116848 x 472998992 x 4043371272 x 3153321488 x 2695581643 x 2441281696 x 2364992543 x 1577282544 x 1576662976 x 1347793286 x 1220644929 x 813765086 x 788645088 x 788336572 x 610327629 x 525769858 x 4068810172 x 3943213144 x 3051615258 x 2628819716 x 20344
Negative: -1 x -401102304-2 x -200551152-3 x -133700768-4 x -100275576-6 x -66850384-8 x -50137788-12 x -33425192-16 x -25068894-24 x -16712596-31 x -12938784-32 x -12534447-48 x -8356298-53 x -7567968-62 x -6469392-93 x -4312928-96 x -4178149-106 x -3783984-124 x -3234696-159 x -2522656-186 x -2156464-212 x -1891992-248 x -1617348-318 x -1261328-372 x -1078232-424 x -945996-496 x -808674-636 x -630664-744 x -539116-848 x -472998-992 x -404337-1272 x -315332-1488 x -269558-1643 x -244128-1696 x -236499-2543 x -157728-2544 x -157666-2976 x -134779-3286 x -122064-4929 x -81376-5086 x -78864-5088 x -78833-6572 x -61032-7629 x -52576-9858 x -40688-10172 x -39432-13144 x -30516-15258 x -26288-19716 x -20344


How do I find the factor combinations of the number 401,102,304?

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 401,102,304, 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.

1 401,102,304
-1 -401,102,304

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 401,102,304.

Example:
1 x 401,102,304 = 401,102,304
and
-1 x -401,102,304 = 401,102,304
Notice both answers equal 401,102,304

With that explanation out of the way, let's continue. Next, we take the number 401,102,304 and divide it by 2:

401,102,304 ÷ 2 = 200,551,152

If the quotient is a whole number, then 2 and 200,551,152 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 2 200,551,152 401,102,304
-1 -2 -200,551,152 -401,102,304

Now, we try dividing 401,102,304 by 3:

401,102,304 ÷ 3 = 133,700,768

If the quotient is a whole number, then 3 and 133,700,768 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 3 133,700,768 200,551,152 401,102,304
-1 -2 -3 -133,700,768 -200,551,152 -401,102,304

Let's try dividing by 4:

401,102,304 ÷ 4 = 100,275,576

If the quotient is a whole number, then 4 and 100,275,576 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 4 100,275,576 133,700,768 200,551,152 401,102,304
-1 -2 -3 -4 -100,275,576 -133,700,768 -200,551,152 401,102,304
Keep dividing by the next highest number until you cannot divide anymore.

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

123468121624313248536293961061241591862122483183724244966367448489921,2721,4881,6431,6962,5432,5442,9763,2864,9295,0865,0886,5727,6299,85810,17213,14415,25819,71620,34426,28830,51639,43240,68852,57661,03278,83378,86481,376122,064134,779157,666157,728236,499244,128269,558315,332404,337472,998539,116630,664808,674945,9961,078,2321,261,3281,617,3481,891,9922,156,4642,522,6563,234,6963,783,9844,178,1494,312,9286,469,3927,567,9688,356,29812,534,44712,938,78416,712,59625,068,89433,425,19250,137,78866,850,384100,275,576133,700,768200,551,152401,102,304
-1-2-3-4-6-8-12-16-24-31-32-48-53-62-93-96-106-124-159-186-212-248-318-372-424-496-636-744-848-992-1,272-1,488-1,643-1,696-2,543-2,544-2,976-3,286-4,929-5,086-5,088-6,572-7,629-9,858-10,172-13,144-15,258-19,716-20,344-26,288-30,516-39,432-40,688-52,576-61,032-78,833-78,864-81,376-122,064-134,779-157,666-157,728-236,499-244,128-269,558-315,332-404,337-472,998-539,116-630,664-808,674-945,996-1,078,232-1,261,328-1,617,348-1,891,992-2,156,464-2,522,656-3,234,696-3,783,984-4,178,149-4,312,928-6,469,392-7,567,968-8,356,298-12,534,447-12,938,784-16,712,596-25,068,894-33,425,192-50,137,788-66,850,384-100,275,576-133,700,768-200,551,152-401,102,304

More Examples

Here are some more numbers to try:

401,102,302401,102,303401,102,305401,102,306
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