Q: What are the factor combinations of the number 517,617,520?

 A:
Positive:   1 x 5176175202 x 2588087604 x 1294043805 x 1035235047 x 739453608 x 6470219010 x 5176175214 x 3697268016 x 3235109520 x 2588087628 x 1848634029 x 1784888035 x 1478907240 x 1294043856 x 924317058 x 892444070 x 739453680 x 6470219112 x 4621585116 x 4462220140 x 3697268145 x 3569776203 x 2549840232 x 2231110280 x 1848634290 x 1784888406 x 1274920464 x 1115555560 x 924317580 x 892444812 x 6374601015 x 5099681160 x 4462221624 x 3187302030 x 2549842320 x 2231113248 x 1593654060 x 1274928120 x 6374616240 x 31873
Negative: -1 x -517617520-2 x -258808760-4 x -129404380-5 x -103523504-7 x -73945360-8 x -64702190-10 x -51761752-14 x -36972680-16 x -32351095-20 x -25880876-28 x -18486340-29 x -17848880-35 x -14789072-40 x -12940438-56 x -9243170-58 x -8924440-70 x -7394536-80 x -6470219-112 x -4621585-116 x -4462220-140 x -3697268-145 x -3569776-203 x -2549840-232 x -2231110-280 x -1848634-290 x -1784888-406 x -1274920-464 x -1115555-560 x -924317-580 x -892444-812 x -637460-1015 x -509968-1160 x -446222-1624 x -318730-2030 x -254984-2320 x -223111-3248 x -159365-4060 x -127492-8120 x -63746-16240 x -31873


How do I find the factor combinations of the number 517,617,520?

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 517,617,520, 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.

1 517,617,520
-1 -517,617,520

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 517,617,520.

Example:
1 x 517,617,520 = 517,617,520
and
-1 x -517,617,520 = 517,617,520
Notice both answers equal 517,617,520

With that explanation out of the way, let's continue. Next, we take the number 517,617,520 and divide it by 2:

517,617,520 ÷ 2 = 258,808,760

If the quotient is a whole number, then 2 and 258,808,760 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 2 258,808,760 517,617,520
-1 -2 -258,808,760 -517,617,520

Now, we try dividing 517,617,520 by 3:

517,617,520 ÷ 3 = 172,539,173.3333

If the quotient is a whole number, then 3 and 172,539,173.3333 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 2 258,808,760 517,617,520
-1 -2 -258,808,760 -517,617,520

Let's try dividing by 4:

517,617,520 ÷ 4 = 129,404,380

If the quotient is a whole number, then 4 and 129,404,380 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 4 129,404,380 258,808,760 517,617,520
-1 -2 -4 -129,404,380 -258,808,760 517,617,520
Keep dividing by the next highest number until you cannot divide anymore.

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

1245781014162028293540565870801121161401452032322802904064645605808121,0151,1601,6242,0302,3203,2484,0608,12016,24031,87363,746127,492159,365223,111254,984318,730446,222509,968637,460892,444924,3171,115,5551,274,9201,784,8881,848,6342,231,1102,549,8403,569,7763,697,2684,462,2204,621,5856,470,2197,394,5368,924,4409,243,17012,940,43814,789,07217,848,88018,486,34025,880,87632,351,09536,972,68051,761,75264,702,19073,945,360103,523,504129,404,380258,808,760517,617,520
-1-2-4-5-7-8-10-14-16-20-28-29-35-40-56-58-70-80-112-116-140-145-203-232-280-290-406-464-560-580-812-1,015-1,160-1,624-2,030-2,320-3,248-4,060-8,120-16,240-31,873-63,746-127,492-159,365-223,111-254,984-318,730-446,222-509,968-637,460-892,444-924,317-1,115,555-1,274,920-1,784,888-1,848,634-2,231,110-2,549,840-3,569,776-3,697,268-4,462,220-4,621,585-6,470,219-7,394,536-8,924,440-9,243,170-12,940,438-14,789,072-17,848,880-18,486,340-25,880,876-32,351,095-36,972,680-51,761,752-64,702,190-73,945,360-103,523,504-129,404,380-258,808,760-517,617,520

More Examples

Here are some more numbers to try:

517,617,518517,617,519517,617,521517,617,522
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