Q: What are the factor combinations of the number 35,767,225?

 A:
Positive:   1 x 357672255 x 715344513 x 275132525 x 143068965 x 550265167 x 214175325 x 110053659 x 54275835 x 428352171 x 164753295 x 108554175 x 8567
Negative: -1 x -35767225-5 x -7153445-13 x -2751325-25 x -1430689-65 x -550265-167 x -214175-325 x -110053-659 x -54275-835 x -42835-2171 x -16475-3295 x -10855-4175 x -8567


How do I find the factor combinations of the number 35,767,225?

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 35,767,225, 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 35,767,225
-1 -35,767,225

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 35,767,225.

Example:
1 x 35,767,225 = 35,767,225
and
-1 x -35,767,225 = 35,767,225
Notice both answers equal 35,767,225

With that explanation out of the way, let's continue. Next, we take the number 35,767,225 and divide it by 2:

35,767,225 ÷ 2 = 17,883,612.5

If the quotient is a whole number, then 2 and 17,883,612.5 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 35,767,225
-1 -35,767,225

Now, we try dividing 35,767,225 by 3:

35,767,225 ÷ 3 = 11,922,408.3333

If the quotient is a whole number, then 3 and 11,922,408.3333 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 35,767,225
-1 -35,767,225

Let's try dividing by 4:

35,767,225 ÷ 4 = 8,941,806.25

If the quotient is a whole number, then 4 and 8,941,806.25 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 35,767,225
-1 35,767,225
Keep dividing by the next highest number until you cannot divide anymore.

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

151325651673256598352,1713,2954,1758,56710,85516,47542,83554,275110,053214,175550,2651,430,6892,751,3257,153,44535,767,225
-1-5-13-25-65-167-325-659-835-2,171-3,295-4,175-8,567-10,855-16,475-42,835-54,275-110,053-214,175-550,265-1,430,689-2,751,325-7,153,445-35,767,225

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