Q: What are the factor combinations of the number 349,525?

 A:
Positive:   1 x 3495255 x 6990511 x 3177525 x 1398131 x 1127541 x 852555 x 6355155 x 2255205 x 1705275 x 1271341 x 1025451 x 775
Negative: -1 x -349525-5 x -69905-11 x -31775-25 x -13981-31 x -11275-41 x -8525-55 x -6355-155 x -2255-205 x -1705-275 x -1271-341 x -1025-451 x -775


How do I find the factor combinations of the number 349,525?

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 349,525, 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.

1 349,525
-1 -349,525

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 349,525.

Example:
1 x 349,525 = 349,525
and
-1 x -349,525 = 349,525
Notice both answers equal 349,525

With that explanation out of the way, let's continue. Next, we take the number 349,525 and divide it by 2:

349,525 ÷ 2 = 174,762.5

If the quotient is a whole number, then 2 and 174,762.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 349,525
-1 -349,525

Now, we try dividing 349,525 by 3:

349,525 ÷ 3 = 116,508.3333

If the quotient is a whole number, then 3 and 116,508.3333 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 349,525
-1 -349,525

Let's try dividing by 4:

349,525 ÷ 4 = 87,381.25

If the quotient is a whole number, then 4 and 87,381.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 349,525
-1 349,525
Keep dividing by the next highest number until you cannot divide anymore.

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

1511253141551552052753414517751,0251,2711,7052,2556,3558,52511,27513,98131,77569,905349,525
-1-5-11-25-31-41-55-155-205-275-341-451-775-1,025-1,271-1,705-2,255-6,355-8,525-11,275-13,981-31,775-69,905-349,525

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