Q: What are the factor combinations of the number 243,038,419?

 A:
Positive:   1 x 24303841913 x 1869526331 x 7839949283 x 858793403 x 6030732131 x 1140493679 x 660618773 x 27703
Negative: -1 x -243038419-13 x -18695263-31 x -7839949-283 x -858793-403 x -603073-2131 x -114049-3679 x -66061-8773 x -27703


How do I find the factor combinations of the number 243,038,419?

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 243,038,419, 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.

1 243,038,419
-1 -243,038,419

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 243,038,419.

Example:
1 x 243,038,419 = 243,038,419
and
-1 x -243,038,419 = 243,038,419
Notice both answers equal 243,038,419

With that explanation out of the way, let's continue. Next, we take the number 243,038,419 and divide it by 2:

243,038,419 ÷ 2 = 121,519,209.5

If the quotient is a whole number, then 2 and 121,519,209.5 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:

1 243,038,419
-1 -243,038,419

Now, we try dividing 243,038,419 by 3:

243,038,419 ÷ 3 = 81,012,806.3333

If the quotient is a whole number, then 3 and 81,012,806.3333 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:

1 243,038,419
-1 -243,038,419

Let's try dividing by 4:

243,038,419 ÷ 4 = 60,759,604.75

If the quotient is a whole number, then 4 and 60,759,604.75 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:

1 243,038,419
-1 243,038,419
Keep dividing by the next highest number until you cannot divide anymore.

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

113312834032,1313,6798,77327,70366,061114,049603,073858,7937,839,94918,695,263243,038,419
-1-13-31-283-403-2,131-3,679-8,773-27,703-66,061-114,049-603,073-858,793-7,839,949-18,695,263-243,038,419

More Examples

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