Q: What are the factor combinations of the number 150,110,148?

 A:
Positive:   1 x 1501101482 x 750550743 x 500367164 x 375275376 x 2501835812 x 1250917929 x 517621258 x 258810683 x 180855687 x 1725404116 x 1294053166 x 904278174 x 862702249 x 602852332 x 452139348 x 431351498 x 301426996 x 1507132407 x 623644814 x 311825197 x 288847221 x 207889628 x 1559110394 x 14442
Negative: -1 x -150110148-2 x -75055074-3 x -50036716-4 x -37527537-6 x -25018358-12 x -12509179-29 x -5176212-58 x -2588106-83 x -1808556-87 x -1725404-116 x -1294053-166 x -904278-174 x -862702-249 x -602852-332 x -452139-348 x -431351-498 x -301426-996 x -150713-2407 x -62364-4814 x -31182-5197 x -28884-7221 x -20788-9628 x -15591-10394 x -14442


How do I find the factor combinations of the number 150,110,148?

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 150,110,148, 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.

1 150,110,148
-1 -150,110,148

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 150,110,148.

Example:
1 x 150,110,148 = 150,110,148
and
-1 x -150,110,148 = 150,110,148
Notice both answers equal 150,110,148

With that explanation out of the way, let's continue. Next, we take the number 150,110,148 and divide it by 2:

150,110,148 ÷ 2 = 75,055,074

If the quotient is a whole number, then 2 and 75,055,074 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 75,055,074 150,110,148
-1 -2 -75,055,074 -150,110,148

Now, we try dividing 150,110,148 by 3:

150,110,148 ÷ 3 = 50,036,716

If the quotient is a whole number, then 3 and 50,036,716 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 50,036,716 75,055,074 150,110,148
-1 -2 -3 -50,036,716 -75,055,074 -150,110,148

Let's try dividing by 4:

150,110,148 ÷ 4 = 37,527,537

If the quotient is a whole number, then 4 and 37,527,537 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 37,527,537 50,036,716 75,055,074 150,110,148
-1 -2 -3 -4 -37,527,537 -50,036,716 -75,055,074 150,110,148
Keep dividing by the next highest number until you cannot divide anymore.

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

1234612295883871161661742493323484989962,4074,8145,1977,2219,62810,39414,44215,59120,78828,88431,18262,364150,713301,426431,351452,139602,852862,702904,2781,294,0531,725,4041,808,5562,588,1065,176,21212,509,17925,018,35837,527,53750,036,71675,055,074150,110,148
-1-2-3-4-6-12-29-58-83-87-116-166-174-249-332-348-498-996-2,407-4,814-5,197-7,221-9,628-10,394-14,442-15,591-20,788-28,884-31,182-62,364-150,713-301,426-431,351-452,139-602,852-862,702-904,278-1,294,053-1,725,404-1,808,556-2,588,106-5,176,212-12,509,179-25,018,358-37,527,537-50,036,716-75,055,074-150,110,148

More Examples

Here are some more numbers to try:

150,110,146150,110,147150,110,149150,110,150
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