Q: What are the factor combinations of the number 501,525,304?

 A:
Positive:   1 x 5015253042 x 2507626524 x 1253813267 x 716464728 x 6269066314 x 3582323623 x 2180544828 x 1791161829 x 1729397646 x 1090272456 x 895580958 x 864698892 x 5451362116 x 4323494161 x 3115064184 x 2725681203 x 2470568232 x 2161747322 x 1557532406 x 1235284463 x 1083208644 x 778766667 x 751912812 x 617642841 x 596344926 x 5416041288 x 3893831334 x 3759561624 x 3088211682 x 2981721852 x 2708022668 x 1879783241 x 1547443364 x 1490863704 x 1354014669 x 1074165336 x 939895887 x 851926482 x 773726728 x 745439338 x 5370810649 x 4709611774 x 4259612964 x 3868613427 x 3735218676 x 2685419343 x 2592821298 x 23548
Negative: -1 x -501525304-2 x -250762652-4 x -125381326-7 x -71646472-8 x -62690663-14 x -35823236-23 x -21805448-28 x -17911618-29 x -17293976-46 x -10902724-56 x -8955809-58 x -8646988-92 x -5451362-116 x -4323494-161 x -3115064-184 x -2725681-203 x -2470568-232 x -2161747-322 x -1557532-406 x -1235284-463 x -1083208-644 x -778766-667 x -751912-812 x -617642-841 x -596344-926 x -541604-1288 x -389383-1334 x -375956-1624 x -308821-1682 x -298172-1852 x -270802-2668 x -187978-3241 x -154744-3364 x -149086-3704 x -135401-4669 x -107416-5336 x -93989-5887 x -85192-6482 x -77372-6728 x -74543-9338 x -53708-10649 x -47096-11774 x -42596-12964 x -38686-13427 x -37352-18676 x -26854-19343 x -25928-21298 x -23548


How do I find the factor combinations of the number 501,525,304?

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 501,525,304, 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.

1 501,525,304
-1 -501,525,304

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 501,525,304.

Example:
1 x 501,525,304 = 501,525,304
and
-1 x -501,525,304 = 501,525,304
Notice both answers equal 501,525,304

With that explanation out of the way, let's continue. Next, we take the number 501,525,304 and divide it by 2:

501,525,304 ÷ 2 = 250,762,652

If the quotient is a whole number, then 2 and 250,762,652 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 2 250,762,652 501,525,304
-1 -2 -250,762,652 -501,525,304

Now, we try dividing 501,525,304 by 3:

501,525,304 ÷ 3 = 167,175,101.3333

If the quotient is a whole number, then 3 and 167,175,101.3333 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 2 250,762,652 501,525,304
-1 -2 -250,762,652 -501,525,304

Let's try dividing by 4:

501,525,304 ÷ 4 = 125,381,326

If the quotient is a whole number, then 4 and 125,381,326 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 4 125,381,326 250,762,652 501,525,304
-1 -2 -4 -125,381,326 -250,762,652 501,525,304
Keep dividing by the next highest number until you cannot divide anymore.

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

1247814232829465658921161611842032323224064636446678128419261,2881,3341,6241,6821,8522,6683,2413,3643,7044,6695,3365,8876,4826,7289,33810,64911,77412,96413,42718,67619,34321,29823,54825,92826,85437,35238,68642,59647,09653,70874,54377,37285,19293,989107,416135,401149,086154,744187,978270,802298,172308,821375,956389,383541,604596,344617,642751,912778,7661,083,2081,235,2841,557,5322,161,7472,470,5682,725,6813,115,0644,323,4945,451,3628,646,9888,955,80910,902,72417,293,97617,911,61821,805,44835,823,23662,690,66371,646,472125,381,326250,762,652501,525,304
-1-2-4-7-8-14-23-28-29-46-56-58-92-116-161-184-203-232-322-406-463-644-667-812-841-926-1,288-1,334-1,624-1,682-1,852-2,668-3,241-3,364-3,704-4,669-5,336-5,887-6,482-6,728-9,338-10,649-11,774-12,964-13,427-18,676-19,343-21,298-23,548-25,928-26,854-37,352-38,686-42,596-47,096-53,708-74,543-77,372-85,192-93,989-107,416-135,401-149,086-154,744-187,978-270,802-298,172-308,821-375,956-389,383-541,604-596,344-617,642-751,912-778,766-1,083,208-1,235,284-1,557,532-2,161,747-2,470,568-2,725,681-3,115,064-4,323,494-5,451,362-8,646,988-8,955,809-10,902,724-17,293,976-17,911,618-21,805,448-35,823,236-62,690,663-71,646,472-125,381,326-250,762,652-501,525,304

More Examples

Here are some more numbers to try:

501,525,302501,525,303501,525,305501,525,306
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