Q: What are the factor combinations of the number 500,220,504?

 A:
Positive:   1 x 5002205042 x 2501102523 x 1667401684 x 1250551266 x 833700847 x 714600728 x 625275639 x 5558005612 x 4168504214 x 3573003618 x 2779002821 x 2382002424 x 2084252128 x 1786501836 x 1389501442 x 1191001256 x 893250963 x 794000872 x 694750784 x 5955006126 x 3970004168 x 2977503173 x 2891448252 x 1985002346 x 1445724504 x 992501519 x 963816692 x 7228621038 x 4819081211 x 4130641384 x 3614311557 x 3212722076 x 2409542422 x 2065323114 x 1606363633 x 1376884152 x 1204774844 x 1032665737 x 871926228 x 803187266 x 688449688 x 5163310899 x 4589611474 x 4359612456 x 4015914532 x 3442217211 x 2906421798 x 22948
Negative: -1 x -500220504-2 x -250110252-3 x -166740168-4 x -125055126-6 x -83370084-7 x -71460072-8 x -62527563-9 x -55580056-12 x -41685042-14 x -35730036-18 x -27790028-21 x -23820024-24 x -20842521-28 x -17865018-36 x -13895014-42 x -11910012-56 x -8932509-63 x -7940008-72 x -6947507-84 x -5955006-126 x -3970004-168 x -2977503-173 x -2891448-252 x -1985002-346 x -1445724-504 x -992501-519 x -963816-692 x -722862-1038 x -481908-1211 x -413064-1384 x -361431-1557 x -321272-2076 x -240954-2422 x -206532-3114 x -160636-3633 x -137688-4152 x -120477-4844 x -103266-5737 x -87192-6228 x -80318-7266 x -68844-9688 x -51633-10899 x -45896-11474 x -43596-12456 x -40159-14532 x -34422-17211 x -29064-21798 x -22948


How do I find the factor combinations of the number 500,220,504?

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 500,220,504, 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.

1 500,220,504
-1 -500,220,504

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 500,220,504.

Example:
1 x 500,220,504 = 500,220,504
and
-1 x -500,220,504 = 500,220,504
Notice both answers equal 500,220,504

With that explanation out of the way, let's continue. Next, we take the number 500,220,504 and divide it by 2:

500,220,504 ÷ 2 = 250,110,252

If the quotient is a whole number, then 2 and 250,110,252 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 2 250,110,252 500,220,504
-1 -2 -250,110,252 -500,220,504

Now, we try dividing 500,220,504 by 3:

500,220,504 ÷ 3 = 166,740,168

If the quotient is a whole number, then 3 and 166,740,168 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 3 166,740,168 250,110,252 500,220,504
-1 -2 -3 -166,740,168 -250,110,252 -500,220,504

Let's try dividing by 4:

500,220,504 ÷ 4 = 125,055,126

If the quotient is a whole number, then 4 and 125,055,126 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 4 125,055,126 166,740,168 250,110,252 500,220,504
-1 -2 -3 -4 -125,055,126 -166,740,168 -250,110,252 500,220,504
Keep dividing by the next highest number until you cannot divide anymore.

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

123467891214182124283642566372841261681732523465045196921,0381,2111,3841,5572,0762,4223,1143,6334,1524,8445,7376,2287,2669,68810,89911,47412,45614,53217,21121,79822,94829,06434,42240,15943,59645,89651,63368,84480,31887,192103,266120,477137,688160,636206,532240,954321,272361,431413,064481,908722,862963,816992,5011,445,7241,985,0022,891,4482,977,5033,970,0045,955,0066,947,5077,940,0088,932,50911,910,01213,895,01417,865,01820,842,52123,820,02427,790,02835,730,03641,685,04255,580,05662,527,56371,460,07283,370,084125,055,126166,740,168250,110,252500,220,504
-1-2-3-4-6-7-8-9-12-14-18-21-24-28-36-42-56-63-72-84-126-168-173-252-346-504-519-692-1,038-1,211-1,384-1,557-2,076-2,422-3,114-3,633-4,152-4,844-5,737-6,228-7,266-9,688-10,899-11,474-12,456-14,532-17,211-21,798-22,948-29,064-34,422-40,159-43,596-45,896-51,633-68,844-80,318-87,192-103,266-120,477-137,688-160,636-206,532-240,954-321,272-361,431-413,064-481,908-722,862-963,816-992,501-1,445,724-1,985,002-2,891,448-2,977,503-3,970,004-5,955,006-6,947,507-7,940,008-8,932,509-11,910,012-13,895,014-17,865,018-20,842,521-23,820,024-27,790,028-35,730,036-41,685,042-55,580,056-62,527,563-71,460,072-83,370,084-125,055,126-166,740,168-250,110,252-500,220,504

More Examples

Here are some more numbers to try:

500,220,502500,220,503500,220,505500,220,506
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