Q: What are the factor combinations of the number 684,684?

 A:
Positive:   1 x 6846842 x 3423423 x 2282284 x 1711716 x 1141147 x 978129 x 7607611 x 6224412 x 5705713 x 5266814 x 4890618 x 3803819 x 3603621 x 3260422 x 3112226 x 2633428 x 2445333 x 2074836 x 1901938 x 1801839 x 1755642 x 1630244 x 1556152 x 1316757 x 1201263 x 1086866 x 1037476 x 900977 x 889278 x 877884 x 815191 x 752499 x 6916114 x 6006117 x 5852126 x 5434132 x 5187133 x 5148143 x 4788154 x 4446156 x 4389171 x 4004182 x 3762198 x 3458209 x 3276228 x 3003231 x 2964234 x 2926247 x 2772252 x 2717266 x 2574273 x 2508286 x 2394308 x 2223342 x 2002364 x 1881396 x 1729399 x 1716418 x 1638429 x 1596462 x 1482468 x 1463494 x 1386532 x 1287546 x 1254572 x 1197627 x 1092684 x 1001693 x 988741 x 924798 x 858819 x 836
Negative: -1 x -684684-2 x -342342-3 x -228228-4 x -171171-6 x -114114-7 x -97812-9 x -76076-11 x -62244-12 x -57057-13 x -52668-14 x -48906-18 x -38038-19 x -36036-21 x -32604-22 x -31122-26 x -26334-28 x -24453-33 x -20748-36 x -19019-38 x -18018-39 x -17556-42 x -16302-44 x -15561-52 x -13167-57 x -12012-63 x -10868-66 x -10374-76 x -9009-77 x -8892-78 x -8778-84 x -8151-91 x -7524-99 x -6916-114 x -6006-117 x -5852-126 x -5434-132 x -5187-133 x -5148-143 x -4788-154 x -4446-156 x -4389-171 x -4004-182 x -3762-198 x -3458-209 x -3276-228 x -3003-231 x -2964-234 x -2926-247 x -2772-252 x -2717-266 x -2574-273 x -2508-286 x -2394-308 x -2223-342 x -2002-364 x -1881-396 x -1729-399 x -1716-418 x -1638-429 x -1596-462 x -1482-468 x -1463-494 x -1386-532 x -1287-546 x -1254-572 x -1197-627 x -1092-684 x -1001-693 x -988-741 x -924-798 x -858-819 x -836


How do I find the factor combinations of the number 684,684?

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 684,684, 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.

1 684,684
-1 -684,684

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 684,684.

Example:
1 x 684,684 = 684,684
and
-1 x -684,684 = 684,684
Notice both answers equal 684,684

With that explanation out of the way, let's continue. Next, we take the number 684,684 and divide it by 2:

684,684 ÷ 2 = 342,342

If the quotient is a whole number, then 2 and 342,342 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 2 342,342 684,684
-1 -2 -342,342 -684,684

Now, we try dividing 684,684 by 3:

684,684 ÷ 3 = 228,228

If the quotient is a whole number, then 3 and 228,228 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 3 228,228 342,342 684,684
-1 -2 -3 -228,228 -342,342 -684,684

Let's try dividing by 4:

684,684 ÷ 4 = 171,171

If the quotient is a whole number, then 4 and 171,171 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 4 171,171 228,228 342,342 684,684
-1 -2 -3 -4 -171,171 -228,228 -342,342 684,684
Keep dividing by the next highest number until you cannot divide anymore.

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

123467911121314181921222628333638394244525763667677788491991141171261321331431541561711821982092282312342472522662732863083423643963994184294624684945325465726276846937417988198368589249881,0011,0921,1971,2541,2871,3861,4631,4821,5961,6381,7161,7291,8812,0022,2232,3942,5082,5742,7172,7722,9262,9643,0033,2763,4583,7624,0044,3894,4464,7885,1485,1875,4345,8526,0066,9167,5248,1518,7788,8929,00910,37410,86812,01213,16715,56116,30217,55618,01819,01920,74824,45326,33431,12232,60436,03638,03848,90652,66857,05762,24476,07697,812114,114171,171228,228342,342684,684
-1-2-3-4-6-7-9-11-12-13-14-18-19-21-22-26-28-33-36-38-39-42-44-52-57-63-66-76-77-78-84-91-99-114-117-126-132-133-143-154-156-171-182-198-209-228-231-234-247-252-266-273-286-308-342-364-396-399-418-429-462-468-494-532-546-572-627-684-693-741-798-819-836-858-924-988-1,001-1,092-1,197-1,254-1,287-1,386-1,463-1,482-1,596-1,638-1,716-1,729-1,881-2,002-2,223-2,394-2,508-2,574-2,717-2,772-2,926-2,964-3,003-3,276-3,458-3,762-4,004-4,389-4,446-4,788-5,148-5,187-5,434-5,852-6,006-6,916-7,524-8,151-8,778-8,892-9,009-10,374-10,868-12,012-13,167-15,561-16,302-17,556-18,018-19,019-20,748-24,453-26,334-31,122-32,604-36,036-38,038-48,906-52,668-57,057-62,244-76,076-97,812-114,114-171,171-228,228-342,342-684,684

More Examples

Here are some more numbers to try:

684,682684,683684,685684,686
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