Q: What are the factor combinations of the number 145,000,512?

 A:
Positive:   1 x 1450005122 x 725002563 x 483335044 x 362501286 x 241667528 x 181250649 x 1611116812 x 1208337616 x 906253218 x 805558424 x 604168832 x 453126636 x 402779248 x 302084464 x 226563372 x 201389696 x 1510422144 x 1006948192 x 755211288 x 503474576 x 251737
Negative: -1 x -145000512-2 x -72500256-3 x -48333504-4 x -36250128-6 x -24166752-8 x -18125064-9 x -16111168-12 x -12083376-16 x -9062532-18 x -8055584-24 x -6041688-32 x -4531266-36 x -4027792-48 x -3020844-64 x -2265633-72 x -2013896-96 x -1510422-144 x -1006948-192 x -755211-288 x -503474-576 x -251737


How do I find the factor combinations of the number 145,000,512?

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 145,000,512, 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.

1 145,000,512
-1 -145,000,512

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 145,000,512.

Example:
1 x 145,000,512 = 145,000,512
and
-1 x -145,000,512 = 145,000,512
Notice both answers equal 145,000,512

With that explanation out of the way, let's continue. Next, we take the number 145,000,512 and divide it by 2:

145,000,512 ÷ 2 = 72,500,256

If the quotient is a whole number, then 2 and 72,500,256 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 72,500,256 145,000,512
-1 -2 -72,500,256 -145,000,512

Now, we try dividing 145,000,512 by 3:

145,000,512 ÷ 3 = 48,333,504

If the quotient is a whole number, then 3 and 48,333,504 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 48,333,504 72,500,256 145,000,512
-1 -2 -3 -48,333,504 -72,500,256 -145,000,512

Let's try dividing by 4:

145,000,512 ÷ 4 = 36,250,128

If the quotient is a whole number, then 4 and 36,250,128 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 36,250,128 48,333,504 72,500,256 145,000,512
-1 -2 -3 -4 -36,250,128 -48,333,504 -72,500,256 145,000,512
Keep dividing by the next highest number until you cannot divide anymore.

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

123468912161824323648647296144192288576251,737503,474755,2111,006,9481,510,4222,013,8962,265,6333,020,8444,027,7924,531,2666,041,6888,055,5849,062,53212,083,37616,111,16818,125,06424,166,75236,250,12848,333,50472,500,256145,000,512
-1-2-3-4-6-8-9-12-16-18-24-32-36-48-64-72-96-144-192-288-576-251,737-503,474-755,211-1,006,948-1,510,422-2,013,896-2,265,633-3,020,844-4,027,792-4,531,266-6,041,688-8,055,584-9,062,532-12,083,376-16,111,168-18,125,064-24,166,752-36,250,128-48,333,504-72,500,256-145,000,512

More Examples

Here are some more numbers to try:

145,000,510145,000,511145,000,513145,000,514
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