Q: What are the factor combinations of the number 505,330,416?

 A:
Positive:   1 x 5053304162 x 2526652083 x 1684434724 x 1263326046 x 842217368 x 631663029 x 5614782412 x 4211086816 x 3158315118 x 2807391224 x 2105543436 x 1403695648 x 1052771772 x 7018478144 x 3509239601 x 8408161202 x 4204081803 x 2802722404 x 2102043606 x 1401364808 x 1051025409 x 934245839 x 865447212 x 700689616 x 5255110818 x 4671211678 x 4327214424 x 3503417517 x 2884821636 x 23356
Negative: -1 x -505330416-2 x -252665208-3 x -168443472-4 x -126332604-6 x -84221736-8 x -63166302-9 x -56147824-12 x -42110868-16 x -31583151-18 x -28073912-24 x -21055434-36 x -14036956-48 x -10527717-72 x -7018478-144 x -3509239-601 x -840816-1202 x -420408-1803 x -280272-2404 x -210204-3606 x -140136-4808 x -105102-5409 x -93424-5839 x -86544-7212 x -70068-9616 x -52551-10818 x -46712-11678 x -43272-14424 x -35034-17517 x -28848-21636 x -23356


How do I find the factor combinations of the number 505,330,416?

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 505,330,416, 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.

1 505,330,416
-1 -505,330,416

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 505,330,416.

Example:
1 x 505,330,416 = 505,330,416
and
-1 x -505,330,416 = 505,330,416
Notice both answers equal 505,330,416

With that explanation out of the way, let's continue. Next, we take the number 505,330,416 and divide it by 2:

505,330,416 ÷ 2 = 252,665,208

If the quotient is a whole number, then 2 and 252,665,208 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 2 252,665,208 505,330,416
-1 -2 -252,665,208 -505,330,416

Now, we try dividing 505,330,416 by 3:

505,330,416 ÷ 3 = 168,443,472

If the quotient is a whole number, then 3 and 168,443,472 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 3 168,443,472 252,665,208 505,330,416
-1 -2 -3 -168,443,472 -252,665,208 -505,330,416

Let's try dividing by 4:

505,330,416 ÷ 4 = 126,332,604

If the quotient is a whole number, then 4 and 126,332,604 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 4 126,332,604 168,443,472 252,665,208 505,330,416
-1 -2 -3 -4 -126,332,604 -168,443,472 -252,665,208 505,330,416
Keep dividing by the next highest number until you cannot divide anymore.

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

1234689121618243648721446011,2021,8032,4043,6064,8085,4095,8397,2129,61610,81811,67814,42417,51721,63623,35628,84835,03443,27246,71252,55170,06886,54493,424105,102140,136210,204280,272420,408840,8163,509,2397,018,47810,527,71714,036,95621,055,43428,073,91231,583,15142,110,86856,147,82463,166,30284,221,736126,332,604168,443,472252,665,208505,330,416
-1-2-3-4-6-8-9-12-16-18-24-36-48-72-144-601-1,202-1,803-2,404-3,606-4,808-5,409-5,839-7,212-9,616-10,818-11,678-14,424-17,517-21,636-23,356-28,848-35,034-43,272-46,712-52,551-70,068-86,544-93,424-105,102-140,136-210,204-280,272-420,408-840,816-3,509,239-7,018,478-10,527,717-14,036,956-21,055,434-28,073,912-31,583,151-42,110,868-56,147,824-63,166,302-84,221,736-126,332,604-168,443,472-252,665,208-505,330,416

More Examples

Here are some more numbers to try:

505,330,414505,330,415505,330,417505,330,418
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