Q: What are the factor combinations of the number 105,060?

 A:
Positive:   1 x 1050602 x 525303 x 350204 x 262655 x 210126 x 1751010 x 1050612 x 875515 x 700417 x 618020 x 525330 x 350234 x 309051 x 206060 x 175168 x 154585 x 1236102 x 1030103 x 1020170 x 618204 x 515206 x 510255 x 412309 x 340
Negative: -1 x -105060-2 x -52530-3 x -35020-4 x -26265-5 x -21012-6 x -17510-10 x -10506-12 x -8755-15 x -7004-17 x -6180-20 x -5253-30 x -3502-34 x -3090-51 x -2060-60 x -1751-68 x -1545-85 x -1236-102 x -1030-103 x -1020-170 x -618-204 x -515-206 x -510-255 x -412-309 x -340


How do I find the factor combinations of the number 105,060?

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 105,060, 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.

1 105,060
-1 -105,060

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 105,060.

Example:
1 x 105,060 = 105,060
and
-1 x -105,060 = 105,060
Notice both answers equal 105,060

With that explanation out of the way, let's continue. Next, we take the number 105,060 and divide it by 2:

105,060 ÷ 2 = 52,530

If the quotient is a whole number, then 2 and 52,530 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 52,530 105,060
-1 -2 -52,530 -105,060

Now, we try dividing 105,060 by 3:

105,060 ÷ 3 = 35,020

If the quotient is a whole number, then 3 and 35,020 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 35,020 52,530 105,060
-1 -2 -3 -35,020 -52,530 -105,060

Let's try dividing by 4:

105,060 ÷ 4 = 26,265

If the quotient is a whole number, then 4 and 26,265 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 26,265 35,020 52,530 105,060
-1 -2 -3 -4 -26,265 -35,020 -52,530 105,060
Keep dividing by the next highest number until you cannot divide anymore.

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

12345610121517203034516068851021031702042062553093404125105156181,0201,0301,2361,5451,7512,0603,0903,5025,2536,1807,0048,75510,50617,51021,01226,26535,02052,530105,060
-1-2-3-4-5-6-10-12-15-17-20-30-34-51-60-68-85-102-103-170-204-206-255-309-340-412-510-515-618-1,020-1,030-1,236-1,545-1,751-2,060-3,090-3,502-5,253-6,180-7,004-8,755-10,506-17,510-21,012-26,265-35,020-52,530-105,060

More Examples

Here are some more numbers to try:

105,058105,059105,061105,062
Try the factor calculator

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