Q: What are the factor combinations of the number 45,114,145?

 A:
Positive:   1 x 451141455 x 902282931 x 145529541 x 1100345155 x 291059205 x 220069229 x 197005961 x 469451145 x 394011271 x 354954805 x 93896355 x 7099
Negative: -1 x -45114145-5 x -9022829-31 x -1455295-41 x -1100345-155 x -291059-205 x -220069-229 x -197005-961 x -46945-1145 x -39401-1271 x -35495-4805 x -9389-6355 x -7099


How do I find the factor combinations of the number 45,114,145?

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 45,114,145, 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 45,114,145
-1 -45,114,145

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 45,114,145.

Example:
1 x 45,114,145 = 45,114,145
and
-1 x -45,114,145 = 45,114,145
Notice both answers equal 45,114,145

With that explanation out of the way, let's continue. Next, we take the number 45,114,145 and divide it by 2:

45,114,145 ÷ 2 = 22,557,072.5

If the quotient is a whole number, then 2 and 22,557,072.5 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 45,114,145
-1 -45,114,145

Now, we try dividing 45,114,145 by 3:

45,114,145 ÷ 3 = 15,038,048.3333

If the quotient is a whole number, then 3 and 15,038,048.3333 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 45,114,145
-1 -45,114,145

Let's try dividing by 4:

45,114,145 ÷ 4 = 11,278,536.25

If the quotient is a whole number, then 4 and 11,278,536.25 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 45,114,145
-1 45,114,145
Keep dividing by the next highest number until you cannot divide anymore.

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

1531411552052299611,1451,2714,8056,3557,0999,38935,49539,40146,945197,005220,069291,0591,100,3451,455,2959,022,82945,114,145
-1-5-31-41-155-205-229-961-1,145-1,271-4,805-6,355-7,099-9,389-35,495-39,401-46,945-197,005-220,069-291,059-1,100,345-1,455,295-9,022,829-45,114,145

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