Q: What are the factor combinations of the number 4,224,025?

 A:
Positive:   1 x 42240255 x 84480513 x 32492525 x 16896141 x 10302565 x 64985205 x 20605317 x 13325325 x 12997533 x 79251025 x 41211585 x 2665
Negative: -1 x -4224025-5 x -844805-13 x -324925-25 x -168961-41 x -103025-65 x -64985-205 x -20605-317 x -13325-325 x -12997-533 x -7925-1025 x -4121-1585 x -2665


How do I find the factor combinations of the number 4,224,025?

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 4,224,025, 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 4,224,025
-1 -4,224,025

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 4,224,025.

Example:
1 x 4,224,025 = 4,224,025
and
-1 x -4,224,025 = 4,224,025
Notice both answers equal 4,224,025

With that explanation out of the way, let's continue. Next, we take the number 4,224,025 and divide it by 2:

4,224,025 ÷ 2 = 2,112,012.5

If the quotient is a whole number, then 2 and 2,112,012.5 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 4,224,025
-1 -4,224,025

Now, we try dividing 4,224,025 by 3:

4,224,025 ÷ 3 = 1,408,008.3333

If the quotient is a whole number, then 3 and 1,408,008.3333 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 4,224,025
-1 -4,224,025

Let's try dividing by 4:

4,224,025 ÷ 4 = 1,056,006.25

If the quotient is a whole number, then 4 and 1,056,006.25 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 4,224,025
-1 4,224,025
Keep dividing by the next highest number until you cannot divide anymore.

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

15132541652053173255331,0251,5852,6654,1217,92512,99713,32520,60564,985103,025168,961324,925844,8054,224,025
-1-5-13-25-41-65-205-317-325-533-1,025-1,585-2,665-4,121-7,925-12,997-13,325-20,605-64,985-103,025-168,961-324,925-844,805-4,224,025

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