Q: What are the factor combinations of the number 420,421,404?

 A:
Positive:   1 x 4204214042 x 2102107023 x 1401404684 x 1051053516 x 7007023412 x 3503511713 x 3234010826 x 1617005439 x 1078003652 x 808502778 x 539001889 x 4723836107 x 3929172156 x 2695009178 x 2361918214 x 1964586267 x 1574612283 x 1485588321 x 1309724356 x 1180959428 x 982293534 x 787306566 x 742794642 x 654862849 x 4951961068 x 3936531132 x 3713971157 x 3633721284 x 3274311391 x 3022441698 x 2475982314 x 1816862782 x 1511223396 x 1237993471 x 1211243679 x 1142764173 x 1007484628 x 908435564 x 755616942 x 605627358 x 571388346 x 503749523 x 4414811037 x 3809213884 x 3028114716 x 2856916692 x 2518719046 x 22074
Negative: -1 x -420421404-2 x -210210702-3 x -140140468-4 x -105105351-6 x -70070234-12 x -35035117-13 x -32340108-26 x -16170054-39 x -10780036-52 x -8085027-78 x -5390018-89 x -4723836-107 x -3929172-156 x -2695009-178 x -2361918-214 x -1964586-267 x -1574612-283 x -1485588-321 x -1309724-356 x -1180959-428 x -982293-534 x -787306-566 x -742794-642 x -654862-849 x -495196-1068 x -393653-1132 x -371397-1157 x -363372-1284 x -327431-1391 x -302244-1698 x -247598-2314 x -181686-2782 x -151122-3396 x -123799-3471 x -121124-3679 x -114276-4173 x -100748-4628 x -90843-5564 x -75561-6942 x -60562-7358 x -57138-8346 x -50374-9523 x -44148-11037 x -38092-13884 x -30281-14716 x -28569-16692 x -25187-19046 x -22074


How do I find the factor combinations of the number 420,421,404?

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 420,421,404, 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.

1 420,421,404
-1 -420,421,404

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 420,421,404.

Example:
1 x 420,421,404 = 420,421,404
and
-1 x -420,421,404 = 420,421,404
Notice both answers equal 420,421,404

With that explanation out of the way, let's continue. Next, we take the number 420,421,404 and divide it by 2:

420,421,404 ÷ 2 = 210,210,702

If the quotient is a whole number, then 2 and 210,210,702 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 2 210,210,702 420,421,404
-1 -2 -210,210,702 -420,421,404

Now, we try dividing 420,421,404 by 3:

420,421,404 ÷ 3 = 140,140,468

If the quotient is a whole number, then 3 and 140,140,468 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 3 140,140,468 210,210,702 420,421,404
-1 -2 -3 -140,140,468 -210,210,702 -420,421,404

Let's try dividing by 4:

420,421,404 ÷ 4 = 105,105,351

If the quotient is a whole number, then 4 and 105,105,351 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 4 105,105,351 140,140,468 210,210,702 420,421,404
-1 -2 -3 -4 -105,105,351 -140,140,468 -210,210,702 420,421,404
Keep dividing by the next highest number until you cannot divide anymore.

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

12346121326395278891071561782142672833213564285345666428491,0681,1321,1571,2841,3911,6982,3142,7823,3963,4713,6794,1734,6285,5646,9427,3588,3469,52311,03713,88414,71616,69219,04622,07425,18728,56930,28138,09244,14850,37457,13860,56275,56190,843100,748114,276121,124123,799151,122181,686247,598302,244327,431363,372371,397393,653495,196654,862742,794787,306982,2931,180,9591,309,7241,485,5881,574,6121,964,5862,361,9182,695,0093,929,1724,723,8365,390,0188,085,02710,780,03616,170,05432,340,10835,035,11770,070,234105,105,351140,140,468210,210,702420,421,404
-1-2-3-4-6-12-13-26-39-52-78-89-107-156-178-214-267-283-321-356-428-534-566-642-849-1,068-1,132-1,157-1,284-1,391-1,698-2,314-2,782-3,396-3,471-3,679-4,173-4,628-5,564-6,942-7,358-8,346-9,523-11,037-13,884-14,716-16,692-19,046-22,074-25,187-28,569-30,281-38,092-44,148-50,374-57,138-60,562-75,561-90,843-100,748-114,276-121,124-123,799-151,122-181,686-247,598-302,244-327,431-363,372-371,397-393,653-495,196-654,862-742,794-787,306-982,293-1,180,959-1,309,724-1,485,588-1,574,612-1,964,586-2,361,918-2,695,009-3,929,172-4,723,836-5,390,018-8,085,027-10,780,036-16,170,054-32,340,108-35,035,117-70,070,234-105,105,351-140,140,468-210,210,702-420,421,404

More Examples

Here are some more numbers to try:

420,421,402420,421,403420,421,405420,421,406
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