Q: What are the factor combinations of the number 40,701,349?

 A:
Positive:   1 x 4070134913 x 313087317 x 239419743 x 946543221 x 184169559 x 72811731 x 556794283 x 9503
Negative: -1 x -40701349-13 x -3130873-17 x -2394197-43 x -946543-221 x -184169-559 x -72811-731 x -55679-4283 x -9503


How do I find the factor combinations of the number 40,701,349?

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 40,701,349, 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 40,701,349
-1 -40,701,349

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 40,701,349.

Example:
1 x 40,701,349 = 40,701,349
and
-1 x -40,701,349 = 40,701,349
Notice both answers equal 40,701,349

With that explanation out of the way, let's continue. Next, we take the number 40,701,349 and divide it by 2:

40,701,349 ÷ 2 = 20,350,674.5

If the quotient is a whole number, then 2 and 20,350,674.5 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 40,701,349
-1 -40,701,349

Now, we try dividing 40,701,349 by 3:

40,701,349 ÷ 3 = 13,567,116.3333

If the quotient is a whole number, then 3 and 13,567,116.3333 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 40,701,349
-1 -40,701,349

Let's try dividing by 4:

40,701,349 ÷ 4 = 10,175,337.25

If the quotient is a whole number, then 4 and 10,175,337.25 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 40,701,349
-1 40,701,349
Keep dividing by the next highest number until you cannot divide anymore.

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

11317432215597314,2839,50355,67972,811184,169946,5432,394,1973,130,87340,701,349
-1-13-17-43-221-559-731-4,283-9,503-55,679-72,811-184,169-946,543-2,394,197-3,130,873-40,701,349

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