Q: What are the factor combinations of the number 4,146,624?

 A:
Positive:   1 x 41466242 x 20733123 x 13822084 x 10366566 x 6911048 x 5183289 x 46073612 x 34555216 x 25916418 x 23036823 x 18028824 x 17277632 x 12958236 x 11518446 x 9014448 x 8638864 x 6479169 x 6009672 x 5759292 x 4507296 x 43194138 x 30048144 x 28796184 x 22536192 x 21597207 x 20032276 x 15024288 x 14398313 x 13248368 x 11268414 x 10016552 x 7512576 x 7199626 x 6624736 x 5634828 x 5008939 x 44161104 x 37561252 x 33121472 x 28171656 x 25041878 x 2208
Negative: -1 x -4146624-2 x -2073312-3 x -1382208-4 x -1036656-6 x -691104-8 x -518328-9 x -460736-12 x -345552-16 x -259164-18 x -230368-23 x -180288-24 x -172776-32 x -129582-36 x -115184-46 x -90144-48 x -86388-64 x -64791-69 x -60096-72 x -57592-92 x -45072-96 x -43194-138 x -30048-144 x -28796-184 x -22536-192 x -21597-207 x -20032-276 x -15024-288 x -14398-313 x -13248-368 x -11268-414 x -10016-552 x -7512-576 x -7199-626 x -6624-736 x -5634-828 x -5008-939 x -4416-1104 x -3756-1252 x -3312-1472 x -2817-1656 x -2504-1878 x -2208


How do I find the factor combinations of the number 4,146,624?

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 4,146,624, 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 4,146,624
-1 -4,146,624

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 4,146,624.

Example:
1 x 4,146,624 = 4,146,624
and
-1 x -4,146,624 = 4,146,624
Notice both answers equal 4,146,624

With that explanation out of the way, let's continue. Next, we take the number 4,146,624 and divide it by 2:

4,146,624 ÷ 2 = 2,073,312

If the quotient is a whole number, then 2 and 2,073,312 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 2,073,312 4,146,624
-1 -2 -2,073,312 -4,146,624

Now, we try dividing 4,146,624 by 3:

4,146,624 ÷ 3 = 1,382,208

If the quotient is a whole number, then 3 and 1,382,208 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 1,382,208 2,073,312 4,146,624
-1 -2 -3 -1,382,208 -2,073,312 -4,146,624

Let's try dividing by 4:

4,146,624 ÷ 4 = 1,036,656

If the quotient is a whole number, then 4 and 1,036,656 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 1,036,656 1,382,208 2,073,312 4,146,624
-1 -2 -3 -4 -1,036,656 -1,382,208 -2,073,312 4,146,624
Keep dividing by the next highest number until you cannot divide anymore.

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

123468912161823243236464864697292961381441841922072762883133684145525766267368289391,1041,2521,4721,6561,8782,2082,5042,8173,3123,7564,4165,0085,6346,6247,1997,51210,01611,26813,24814,39815,02420,03221,59722,53628,79630,04843,19445,07257,59260,09664,79186,38890,144115,184129,582172,776180,288230,368259,164345,552460,736518,328691,1041,036,6561,382,2082,073,3124,146,624
-1-2-3-4-6-8-9-12-16-18-23-24-32-36-46-48-64-69-72-92-96-138-144-184-192-207-276-288-313-368-414-552-576-626-736-828-939-1,104-1,252-1,472-1,656-1,878-2,208-2,504-2,817-3,312-3,756-4,416-5,008-5,634-6,624-7,199-7,512-10,016-11,268-13,248-14,398-15,024-20,032-21,597-22,536-28,796-30,048-43,194-45,072-57,592-60,096-64,791-86,388-90,144-115,184-129,582-172,776-180,288-230,368-259,164-345,552-460,736-518,328-691,104-1,036,656-1,382,208-2,073,312-4,146,624

More Examples

Here are some more numbers to try:

4,146,6224,146,6234,146,6254,146,626
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