Q: What are the factor combinations of the number 101,020,745?

 A:
Positive:   1 x 1010207455 x 202041497 x 1443153535 x 2886307691 x 1461953455 x 292394177 x 241854837 x 20885
Negative: -1 x -101020745-5 x -20204149-7 x -14431535-35 x -2886307-691 x -146195-3455 x -29239-4177 x -24185-4837 x -20885


How do I find the factor combinations of the number 101,020,745?

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 101,020,745, 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.

1 101,020,745
-1 -101,020,745

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 101,020,745.

Example:
1 x 101,020,745 = 101,020,745
and
-1 x -101,020,745 = 101,020,745
Notice both answers equal 101,020,745

With that explanation out of the way, let's continue. Next, we take the number 101,020,745 and divide it by 2:

101,020,745 ÷ 2 = 50,510,372.5

If the quotient is a whole number, then 2 and 50,510,372.5 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:

1 101,020,745
-1 -101,020,745

Now, we try dividing 101,020,745 by 3:

101,020,745 ÷ 3 = 33,673,581.6667

If the quotient is a whole number, then 3 and 33,673,581.6667 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:

1 101,020,745
-1 -101,020,745

Let's try dividing by 4:

101,020,745 ÷ 4 = 25,255,186.25

If the quotient is a whole number, then 4 and 25,255,186.25 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:

1 101,020,745
-1 101,020,745
Keep dividing by the next highest number until you cannot divide anymore.

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

157356913,4554,1774,83720,88524,18529,239146,1952,886,30714,431,53520,204,149101,020,745
-1-5-7-35-691-3,455-4,177-4,837-20,885-24,185-29,239-146,195-2,886,307-14,431,535-20,204,149-101,020,745

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