Q: What are the factor combinations of the number 505,003,520?

 A:
Positive:   1 x 5050035202 x 2525017604 x 1262508805 x 1010007047 x 721433608 x 6312544010 x 5050035214 x 3607168016 x 3156272020 x 2525017628 x 1803584032 x 1578136035 x 1442867240 x 1262508856 x 901792064 x 789068070 x 721433680 x 6312544112 x 4508960128 x 3945340140 x 3607168160 x 3156272224 x 2254480256 x 1972670280 x 1803584320 x 1578136448 x 1127240512 x 986335560 x 901792640 x 789068896 x 5636201120 x 4508961280 x 3945341792 x 2818102240 x 2254482560 x 1972673584 x 1409054480 x 1127248960 x 5636217920 x 28181
Negative: -1 x -505003520-2 x -252501760-4 x -126250880-5 x -101000704-7 x -72143360-8 x -63125440-10 x -50500352-14 x -36071680-16 x -31562720-20 x -25250176-28 x -18035840-32 x -15781360-35 x -14428672-40 x -12625088-56 x -9017920-64 x -7890680-70 x -7214336-80 x -6312544-112 x -4508960-128 x -3945340-140 x -3607168-160 x -3156272-224 x -2254480-256 x -1972670-280 x -1803584-320 x -1578136-448 x -1127240-512 x -986335-560 x -901792-640 x -789068-896 x -563620-1120 x -450896-1280 x -394534-1792 x -281810-2240 x -225448-2560 x -197267-3584 x -140905-4480 x -112724-8960 x -56362-17920 x -28181


How do I find the factor combinations of the number 505,003,520?

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 505,003,520, 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.

1 505,003,520
-1 -505,003,520

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 505,003,520.

Example:
1 x 505,003,520 = 505,003,520
and
-1 x -505,003,520 = 505,003,520
Notice both answers equal 505,003,520

With that explanation out of the way, let's continue. Next, we take the number 505,003,520 and divide it by 2:

505,003,520 ÷ 2 = 252,501,760

If the quotient is a whole number, then 2 and 252,501,760 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 2 252,501,760 505,003,520
-1 -2 -252,501,760 -505,003,520

Now, we try dividing 505,003,520 by 3:

505,003,520 ÷ 3 = 168,334,506.6667

If the quotient is a whole number, then 3 and 168,334,506.6667 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 2 252,501,760 505,003,520
-1 -2 -252,501,760 -505,003,520

Let's try dividing by 4:

505,003,520 ÷ 4 = 126,250,880

If the quotient is a whole number, then 4 and 126,250,880 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 4 126,250,880 252,501,760 505,003,520
-1 -2 -4 -126,250,880 -252,501,760 505,003,520
Keep dividing by the next highest number until you cannot divide anymore.

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

1245781014162028323540566470801121281401602242562803204485125606408961,1201,2801,7922,2402,5603,5844,4808,96017,92028,18156,362112,724140,905197,267225,448281,810394,534450,896563,620789,068901,792986,3351,127,2401,578,1361,803,5841,972,6702,254,4803,156,2723,607,1683,945,3404,508,9606,312,5447,214,3367,890,6809,017,92012,625,08814,428,67215,781,36018,035,84025,250,17631,562,72036,071,68050,500,35263,125,44072,143,360101,000,704126,250,880252,501,760505,003,520
-1-2-4-5-7-8-10-14-16-20-28-32-35-40-56-64-70-80-112-128-140-160-224-256-280-320-448-512-560-640-896-1,120-1,280-1,792-2,240-2,560-3,584-4,480-8,960-17,920-28,181-56,362-112,724-140,905-197,267-225,448-281,810-394,534-450,896-563,620-789,068-901,792-986,335-1,127,240-1,578,136-1,803,584-1,972,670-2,254,480-3,156,272-3,607,168-3,945,340-4,508,960-6,312,544-7,214,336-7,890,680-9,017,920-12,625,088-14,428,672-15,781,360-18,035,840-25,250,176-31,562,720-36,071,680-50,500,352-63,125,440-72,143,360-101,000,704-126,250,880-252,501,760-505,003,520

More Examples

Here are some more numbers to try:

505,003,518505,003,519505,003,521505,003,522
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