Q: What are the factor combinations of the number 429,275?

 A:
Positive:   1 x 4292755 x 858557 x 6132511 x 3902525 x 1717135 x 1226555 x 780577 x 5575175 x 2453223 x 1925275 x 1561385 x 1115
Negative: -1 x -429275-5 x -85855-7 x -61325-11 x -39025-25 x -17171-35 x -12265-55 x -7805-77 x -5575-175 x -2453-223 x -1925-275 x -1561-385 x -1115


How do I find the factor combinations of the number 429,275?

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 429,275, 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.

1 429,275
-1 -429,275

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 429,275.

Example:
1 x 429,275 = 429,275
and
-1 x -429,275 = 429,275
Notice both answers equal 429,275

With that explanation out of the way, let's continue. Next, we take the number 429,275 and divide it by 2:

429,275 ÷ 2 = 214,637.5

If the quotient is a whole number, then 2 and 214,637.5 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:

1 429,275
-1 -429,275

Now, we try dividing 429,275 by 3:

429,275 ÷ 3 = 143,091.6667

If the quotient is a whole number, then 3 and 143,091.6667 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:

1 429,275
-1 -429,275

Let's try dividing by 4:

429,275 ÷ 4 = 107,318.75

If the quotient is a whole number, then 4 and 107,318.75 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:

1 429,275
-1 429,275
Keep dividing by the next highest number until you cannot divide anymore.

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

15711253555771752232753851,1151,5611,9252,4535,5757,80512,26517,17139,02561,32585,855429,275
-1-5-7-11-25-35-55-77-175-223-275-385-1,115-1,561-1,925-2,453-5,575-7,805-12,265-17,171-39,025-61,325-85,855-429,275

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