Q: What are the factor combinations of the number 105,624?

 A:
Positive:   1 x 1056242 x 528123 x 352084 x 264066 x 176048 x 132039 x 1173612 x 880218 x 586824 x 440127 x 391236 x 293454 x 195672 x 146781 x 1304108 x 978162 x 652163 x 648216 x 489324 x 326
Negative: -1 x -105624-2 x -52812-3 x -35208-4 x -26406-6 x -17604-8 x -13203-9 x -11736-12 x -8802-18 x -5868-24 x -4401-27 x -3912-36 x -2934-54 x -1956-72 x -1467-81 x -1304-108 x -978-162 x -652-163 x -648-216 x -489-324 x -326


How do I find the factor combinations of the number 105,624?

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 105,624, 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.

1 105,624
-1 -105,624

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 105,624.

Example:
1 x 105,624 = 105,624
and
-1 x -105,624 = 105,624
Notice both answers equal 105,624

With that explanation out of the way, let's continue. Next, we take the number 105,624 and divide it by 2:

105,624 ÷ 2 = 52,812

If the quotient is a whole number, then 2 and 52,812 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 52,812 105,624
-1 -2 -52,812 -105,624

Now, we try dividing 105,624 by 3:

105,624 ÷ 3 = 35,208

If the quotient is a whole number, then 3 and 35,208 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 35,208 52,812 105,624
-1 -2 -3 -35,208 -52,812 -105,624

Let's try dividing by 4:

105,624 ÷ 4 = 26,406

If the quotient is a whole number, then 4 and 26,406 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 26,406 35,208 52,812 105,624
-1 -2 -3 -4 -26,406 -35,208 -52,812 105,624
Keep dividing by the next highest number until you cannot divide anymore.

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

123468912182427365472811081621632163243264896486529781,3041,4671,9562,9343,9124,4015,8688,80211,73613,20317,60426,40635,20852,812105,624
-1-2-3-4-6-8-9-12-18-24-27-36-54-72-81-108-162-163-216-324-326-489-648-652-978-1,304-1,467-1,956-2,934-3,912-4,401-5,868-8,802-11,736-13,203-17,604-26,406-35,208-52,812-105,624

More Examples

Here are some more numbers to try:

105,622105,623105,625105,626
Try the factor calculator

Explore more about the number 105,624:


Ask a Question