Q: What are the factor combinations of the number 420,050,448?

 A:
Positive:   1 x 4200504482 x 2100252243 x 1400168164 x 1050126126 x 700084088 x 525063069 x 4667227212 x 3500420416 x 2625315318 x 2333613624 x 1750210227 x 1555742436 x 1166806848 x 875105154 x 777871272 x 583403481 x 5185808108 x 3889356144 x 2917017162 x 2592904216 x 1944678324 x 1296452432 x 972339648 x 6482261296 x 324113
Negative: -1 x -420050448-2 x -210025224-3 x -140016816-4 x -105012612-6 x -70008408-8 x -52506306-9 x -46672272-12 x -35004204-16 x -26253153-18 x -23336136-24 x -17502102-27 x -15557424-36 x -11668068-48 x -8751051-54 x -7778712-72 x -5834034-81 x -5185808-108 x -3889356-144 x -2917017-162 x -2592904-216 x -1944678-324 x -1296452-432 x -972339-648 x -648226-1296 x -324113


How do I find the factor combinations of the number 420,050,448?

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 420,050,448, 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.

1 420,050,448
-1 -420,050,448

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 420,050,448.

Example:
1 x 420,050,448 = 420,050,448
and
-1 x -420,050,448 = 420,050,448
Notice both answers equal 420,050,448

With that explanation out of the way, let's continue. Next, we take the number 420,050,448 and divide it by 2:

420,050,448 ÷ 2 = 210,025,224

If the quotient is a whole number, then 2 and 210,025,224 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 2 210,025,224 420,050,448
-1 -2 -210,025,224 -420,050,448

Now, we try dividing 420,050,448 by 3:

420,050,448 ÷ 3 = 140,016,816

If the quotient is a whole number, then 3 and 140,016,816 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 3 140,016,816 210,025,224 420,050,448
-1 -2 -3 -140,016,816 -210,025,224 -420,050,448

Let's try dividing by 4:

420,050,448 ÷ 4 = 105,012,612

If the quotient is a whole number, then 4 and 105,012,612 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 4 105,012,612 140,016,816 210,025,224 420,050,448
-1 -2 -3 -4 -105,012,612 -140,016,816 -210,025,224 420,050,448
Keep dividing by the next highest number until you cannot divide anymore.

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

1234689121618242736485472811081441622163244326481,296324,113648,226972,3391,296,4521,944,6782,592,9042,917,0173,889,3565,185,8085,834,0347,778,7128,751,05111,668,06815,557,42417,502,10223,336,13626,253,15335,004,20446,672,27252,506,30670,008,408105,012,612140,016,816210,025,224420,050,448
-1-2-3-4-6-8-9-12-16-18-24-27-36-48-54-72-81-108-144-162-216-324-432-648-1,296-324,113-648,226-972,339-1,296,452-1,944,678-2,592,904-2,917,017-3,889,356-5,185,808-5,834,034-7,778,712-8,751,051-11,668,068-15,557,424-17,502,102-23,336,136-26,253,153-35,004,204-46,672,272-52,506,306-70,008,408-105,012,612-140,016,816-210,025,224-420,050,448

More Examples

Here are some more numbers to try:

420,050,446420,050,447420,050,449420,050,450
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