Q: What are the factor combinations of the number 675,024,624?

 A:
Positive:   1 x 6750246242 x 3375123123 x 2250082084 x 1687561566 x 1125041048 x 843780789 x 7500273612 x 5625205216 x 4218903918 x 3750136824 x 2812602627 x 2500091236 x 1875068448 x 1406301354 x 1250045672 x 9375342108 x 6250228144 x 4687671216 x 3125114277 x 2436912432 x 1562557554 x 1218456831 x 8123041108 x 6092281662 x 4061522216 x 3046142493 x 2707683324 x 2030764432 x 1523074986 x 1353845641 x 1196646648 x 1015387479 x 902569972 x 6769211282 x 5983213296 x 5076914958 x 4512816923 x 3988819944 x 3384622564 x 29916
Negative: -1 x -675024624-2 x -337512312-3 x -225008208-4 x -168756156-6 x -112504104-8 x -84378078-9 x -75002736-12 x -56252052-16 x -42189039-18 x -37501368-24 x -28126026-27 x -25000912-36 x -18750684-48 x -14063013-54 x -12500456-72 x -9375342-108 x -6250228-144 x -4687671-216 x -3125114-277 x -2436912-432 x -1562557-554 x -1218456-831 x -812304-1108 x -609228-1662 x -406152-2216 x -304614-2493 x -270768-3324 x -203076-4432 x -152307-4986 x -135384-5641 x -119664-6648 x -101538-7479 x -90256-9972 x -67692-11282 x -59832-13296 x -50769-14958 x -45128-16923 x -39888-19944 x -33846-22564 x -29916


How do I find the factor combinations of the number 675,024,624?

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 675,024,624, 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.

1 675,024,624
-1 -675,024,624

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 675,024,624.

Example:
1 x 675,024,624 = 675,024,624
and
-1 x -675,024,624 = 675,024,624
Notice both answers equal 675,024,624

With that explanation out of the way, let's continue. Next, we take the number 675,024,624 and divide it by 2:

675,024,624 ÷ 2 = 337,512,312

If the quotient is a whole number, then 2 and 337,512,312 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 2 337,512,312 675,024,624
-1 -2 -337,512,312 -675,024,624

Now, we try dividing 675,024,624 by 3:

675,024,624 ÷ 3 = 225,008,208

If the quotient is a whole number, then 3 and 225,008,208 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 3 225,008,208 337,512,312 675,024,624
-1 -2 -3 -225,008,208 -337,512,312 -675,024,624

Let's try dividing by 4:

675,024,624 ÷ 4 = 168,756,156

If the quotient is a whole number, then 4 and 168,756,156 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 4 168,756,156 225,008,208 337,512,312 675,024,624
-1 -2 -3 -4 -168,756,156 -225,008,208 -337,512,312 675,024,624
Keep dividing by the next highest number until you cannot divide anymore.

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

12346891216182427364854721081442162774325548311,1081,6622,2162,4933,3244,4324,9865,6416,6487,4799,97211,28213,29614,95816,92319,94422,56429,91633,84639,88845,12850,76959,83267,69290,256101,538119,664135,384152,307203,076270,768304,614406,152609,228812,3041,218,4561,562,5572,436,9123,125,1144,687,6716,250,2289,375,34212,500,45614,063,01318,750,68425,000,91228,126,02637,501,36842,189,03956,252,05275,002,73684,378,078112,504,104168,756,156225,008,208337,512,312675,024,624
-1-2-3-4-6-8-9-12-16-18-24-27-36-48-54-72-108-144-216-277-432-554-831-1,108-1,662-2,216-2,493-3,324-4,432-4,986-5,641-6,648-7,479-9,972-11,282-13,296-14,958-16,923-19,944-22,564-29,916-33,846-39,888-45,128-50,769-59,832-67,692-90,256-101,538-119,664-135,384-152,307-203,076-270,768-304,614-406,152-609,228-812,304-1,218,456-1,562,557-2,436,912-3,125,114-4,687,671-6,250,228-9,375,342-12,500,456-14,063,013-18,750,684-25,000,912-28,126,026-37,501,368-42,189,039-56,252,052-75,002,736-84,378,078-112,504,104-168,756,156-225,008,208-337,512,312-675,024,624

More Examples

Here are some more numbers to try:

675,024,622675,024,623675,024,625675,024,626
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