Q: What are the factor combinations of the number 735,072,541?

 A:
Positive:   1 x 7350725417 x 10501036329 x 25347329137 x 5365493203 x 3621047959 x 7664993973 x 18501726431 x 27811
Negative: -1 x -735072541-7 x -105010363-29 x -25347329-137 x -5365493-203 x -3621047-959 x -766499-3973 x -185017-26431 x -27811


How do I find the factor combinations of the number 735,072,541?

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 735,072,541, 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.

1 735,072,541
-1 -735,072,541

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 735,072,541.

Example:
1 x 735,072,541 = 735,072,541
and
-1 x -735,072,541 = 735,072,541
Notice both answers equal 735,072,541

With that explanation out of the way, let's continue. Next, we take the number 735,072,541 and divide it by 2:

735,072,541 ÷ 2 = 367,536,270.5

If the quotient is a whole number, then 2 and 367,536,270.5 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:

1 735,072,541
-1 -735,072,541

Now, we try dividing 735,072,541 by 3:

735,072,541 ÷ 3 = 245,024,180.3333

If the quotient is a whole number, then 3 and 245,024,180.3333 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:

1 735,072,541
-1 -735,072,541

Let's try dividing by 4:

735,072,541 ÷ 4 = 183,768,135.25

If the quotient is a whole number, then 4 and 183,768,135.25 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:

1 735,072,541
-1 735,072,541
Keep dividing by the next highest number until you cannot divide anymore.

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

17291372039593,97326,43127,811185,017766,4993,621,0475,365,49325,347,329105,010,363735,072,541
-1-7-29-137-203-959-3,973-26,431-27,811-185,017-766,499-3,621,047-5,365,493-25,347,329-105,010,363-735,072,541

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