Q: What are the factor combinations of the number 505,260?

 A:
Positive:   1 x 5052602 x 2526303 x 1684204 x 1263155 x 1010526 x 842107 x 721809 x 5614010 x 5052612 x 4210514 x 3609015 x 3368418 x 2807020 x 2526321 x 2406028 x 1804530 x 1684235 x 1443636 x 1403542 x 1203045 x 1122860 x 842163 x 802070 x 721884 x 601590 x 5614105 x 4812126 x 4010140 x 3609180 x 2807210 x 2406252 x 2005315 x 1604401 x 1260420 x 1203630 x 802
Negative: -1 x -505260-2 x -252630-3 x -168420-4 x -126315-5 x -101052-6 x -84210-7 x -72180-9 x -56140-10 x -50526-12 x -42105-14 x -36090-15 x -33684-18 x -28070-20 x -25263-21 x -24060-28 x -18045-30 x -16842-35 x -14436-36 x -14035-42 x -12030-45 x -11228-60 x -8421-63 x -8020-70 x -7218-84 x -6015-90 x -5614-105 x -4812-126 x -4010-140 x -3609-180 x -2807-210 x -2406-252 x -2005-315 x -1604-401 x -1260-420 x -1203-630 x -802


How do I find the factor combinations of the number 505,260?

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 505,260, 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.

1 505,260
-1 -505,260

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 505,260.

Example:
1 x 505,260 = 505,260
and
-1 x -505,260 = 505,260
Notice both answers equal 505,260

With that explanation out of the way, let's continue. Next, we take the number 505,260 and divide it by 2:

505,260 ÷ 2 = 252,630

If the quotient is a whole number, then 2 and 252,630 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 2 252,630 505,260
-1 -2 -252,630 -505,260

Now, we try dividing 505,260 by 3:

505,260 ÷ 3 = 168,420

If the quotient is a whole number, then 3 and 168,420 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 3 168,420 252,630 505,260
-1 -2 -3 -168,420 -252,630 -505,260

Let's try dividing by 4:

505,260 ÷ 4 = 126,315

If the quotient is a whole number, then 4 and 126,315 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 4 126,315 168,420 252,630 505,260
-1 -2 -3 -4 -126,315 -168,420 -252,630 505,260
Keep dividing by the next highest number until you cannot divide anymore.

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

123456791012141518202128303536424560637084901051261401802102523154014206308021,2031,2601,6042,0052,4062,8073,6094,0104,8125,6146,0157,2188,0208,42111,22812,03014,03514,43616,84218,04524,06025,26328,07033,68436,09042,10550,52656,14072,18084,210101,052126,315168,420252,630505,260
-1-2-3-4-5-6-7-9-10-12-14-15-18-20-21-28-30-35-36-42-45-60-63-70-84-90-105-126-140-180-210-252-315-401-420-630-802-1,203-1,260-1,604-2,005-2,406-2,807-3,609-4,010-4,812-5,614-6,015-7,218-8,020-8,421-11,228-12,030-14,035-14,436-16,842-18,045-24,060-25,263-28,070-33,684-36,090-42,105-50,526-56,140-72,180-84,210-101,052-126,315-168,420-252,630-505,260

More Examples

Here are some more numbers to try:

505,258505,259505,261505,262
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