Q: What are the factor combinations of the number 150,003,138?

 A:
Positive:   1 x 1500031382 x 750015693 x 500010466 x 2500052317 x 882371419 x 789490229 x 517252234 x 441185738 x 394745151 x 294123857 x 263163458 x 258626187 x 1724174102 x 1470619114 x 1315817157 x 955434174 x 862087289 x 519042314 x 477717323 x 464406471 x 318478493 x 304266551 x 272238578 x 259521646 x 232203867 x 173014942 x 159239969 x 154802986 x 1521331102 x 1361191479 x 1014221653 x 907461734 x 865071938 x 774012669 x 562022958 x 507112983 x 502863306 x 453734553 x 329465338 x 281015491 x 273185966 x 251438007 x 187348381 x 178988949 x 167629106 x 164739367 x 1601410982 x 13659
Negative: -1 x -150003138-2 x -75001569-3 x -50001046-6 x -25000523-17 x -8823714-19 x -7894902-29 x -5172522-34 x -4411857-38 x -3947451-51 x -2941238-57 x -2631634-58 x -2586261-87 x -1724174-102 x -1470619-114 x -1315817-157 x -955434-174 x -862087-289 x -519042-314 x -477717-323 x -464406-471 x -318478-493 x -304266-551 x -272238-578 x -259521-646 x -232203-867 x -173014-942 x -159239-969 x -154802-986 x -152133-1102 x -136119-1479 x -101422-1653 x -90746-1734 x -86507-1938 x -77401-2669 x -56202-2958 x -50711-2983 x -50286-3306 x -45373-4553 x -32946-5338 x -28101-5491 x -27318-5966 x -25143-8007 x -18734-8381 x -17898-8949 x -16762-9106 x -16473-9367 x -16014-10982 x -13659


How do I find the factor combinations of the number 150,003,138?

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 150,003,138, 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.

1 150,003,138
-1 -150,003,138

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 150,003,138.

Example:
1 x 150,003,138 = 150,003,138
and
-1 x -150,003,138 = 150,003,138
Notice both answers equal 150,003,138

With that explanation out of the way, let's continue. Next, we take the number 150,003,138 and divide it by 2:

150,003,138 ÷ 2 = 75,001,569

If the quotient is a whole number, then 2 and 75,001,569 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 75,001,569 150,003,138
-1 -2 -75,001,569 -150,003,138

Now, we try dividing 150,003,138 by 3:

150,003,138 ÷ 3 = 50,001,046

If the quotient is a whole number, then 3 and 50,001,046 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 50,001,046 75,001,569 150,003,138
-1 -2 -3 -50,001,046 -75,001,569 -150,003,138

Let's try dividing by 4:

150,003,138 ÷ 4 = 37,500,784.5

If the quotient is a whole number, then 4 and 37,500,784.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 2 3 50,001,046 75,001,569 150,003,138
-1 -2 -3 -50,001,046 -75,001,569 150,003,138
Keep dividing by the next highest number until you cannot divide anymore.

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

12361719293438515758871021141571742893143234714935515786468679429699861,1021,4791,6531,7341,9382,6692,9582,9833,3064,5535,3385,4915,9668,0078,3818,9499,1069,36710,98213,65916,01416,47316,76217,89818,73425,14327,31828,10132,94645,37350,28650,71156,20277,40186,50790,746101,422136,119152,133154,802159,239173,014232,203259,521272,238304,266318,478464,406477,717519,042862,087955,4341,315,8171,470,6191,724,1742,586,2612,631,6342,941,2383,947,4514,411,8575,172,5227,894,9028,823,71425,000,52350,001,04675,001,569150,003,138
-1-2-3-6-17-19-29-34-38-51-57-58-87-102-114-157-174-289-314-323-471-493-551-578-646-867-942-969-986-1,102-1,479-1,653-1,734-1,938-2,669-2,958-2,983-3,306-4,553-5,338-5,491-5,966-8,007-8,381-8,949-9,106-9,367-10,982-13,659-16,014-16,473-16,762-17,898-18,734-25,143-27,318-28,101-32,946-45,373-50,286-50,711-56,202-77,401-86,507-90,746-101,422-136,119-152,133-154,802-159,239-173,014-232,203-259,521-272,238-304,266-318,478-464,406-477,717-519,042-862,087-955,434-1,315,817-1,470,619-1,724,174-2,586,261-2,631,634-2,941,238-3,947,451-4,411,857-5,172,522-7,894,902-8,823,714-25,000,523-50,001,046-75,001,569-150,003,138

More Examples

Here are some more numbers to try:

150,003,136150,003,137150,003,139150,003,140
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