Q: What are the factor combinations of the number 6,421,525?

 A:
Positive:   1 x 64215255 x 128430511 x 58377519 x 33797525 x 25686155 x 11675595 x 67595209 x 30725275 x 23351475 x 135191045 x 61451229 x 5225
Negative: -1 x -6421525-5 x -1284305-11 x -583775-19 x -337975-25 x -256861-55 x -116755-95 x -67595-209 x -30725-275 x -23351-475 x -13519-1045 x -6145-1229 x -5225


How do I find the factor combinations of the number 6,421,525?

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 6,421,525, 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 6,421,525
-1 -6,421,525

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 6,421,525.

Example:
1 x 6,421,525 = 6,421,525
and
-1 x -6,421,525 = 6,421,525
Notice both answers equal 6,421,525

With that explanation out of the way, let's continue. Next, we take the number 6,421,525 and divide it by 2:

6,421,525 ÷ 2 = 3,210,762.5

If the quotient is a whole number, then 2 and 3,210,762.5 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 6,421,525
-1 -6,421,525

Now, we try dividing 6,421,525 by 3:

6,421,525 ÷ 3 = 2,140,508.3333

If the quotient is a whole number, then 3 and 2,140,508.3333 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 6,421,525
-1 -6,421,525

Let's try dividing by 4:

6,421,525 ÷ 4 = 1,605,381.25

If the quotient is a whole number, then 4 and 1,605,381.25 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 6,421,525
-1 6,421,525
Keep dividing by the next highest number until you cannot divide anymore.

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

1511192555952092754751,0451,2295,2256,14513,51923,35130,72567,595116,755256,861337,975583,7751,284,3056,421,525
-1-5-11-19-25-55-95-209-275-475-1,045-1,229-5,225-6,145-13,519-23,351-30,725-67,595-116,755-256,861-337,975-583,775-1,284,305-6,421,525

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