Q: What are the factor combinations of the number 145,424,405?

 A:
Positive:   1 x 1454244055 x 290848817 x 2077491535 x 415498349 x 2967845245 x 593569691 x 210455859 x 1692953455 x 420914295 x 338594837 x 300656013 x 24185
Negative: -1 x -145424405-5 x -29084881-7 x -20774915-35 x -4154983-49 x -2967845-245 x -593569-691 x -210455-859 x -169295-3455 x -42091-4295 x -33859-4837 x -30065-6013 x -24185


How do I find the factor combinations of the number 145,424,405?

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 145,424,405, 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.

1 145,424,405
-1 -145,424,405

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 145,424,405.

Example:
1 x 145,424,405 = 145,424,405
and
-1 x -145,424,405 = 145,424,405
Notice both answers equal 145,424,405

With that explanation out of the way, let's continue. Next, we take the number 145,424,405 and divide it by 2:

145,424,405 ÷ 2 = 72,712,202.5

If the quotient is a whole number, then 2 and 72,712,202.5 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:

1 145,424,405
-1 -145,424,405

Now, we try dividing 145,424,405 by 3:

145,424,405 ÷ 3 = 48,474,801.6667

If the quotient is a whole number, then 3 and 48,474,801.6667 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:

1 145,424,405
-1 -145,424,405

Let's try dividing by 4:

145,424,405 ÷ 4 = 36,356,101.25

If the quotient is a whole number, then 4 and 36,356,101.25 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:

1 145,424,405
-1 145,424,405
Keep dividing by the next highest number until you cannot divide anymore.

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

15735492456918593,4554,2954,8376,01324,18530,06533,85942,091169,295210,455593,5692,967,8454,154,98320,774,91529,084,881145,424,405
-1-5-7-35-49-245-691-859-3,455-4,295-4,837-6,013-24,185-30,065-33,859-42,091-169,295-210,455-593,569-2,967,845-4,154,983-20,774,915-29,084,881-145,424,405

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