Q: What are the factor combinations of the number 31,407,475?

 A:
Positive:   1 x 314074755 x 628149511 x 285522519 x 165302525 x 125629955 x 57104595 x 330605209 x 150275275 x 114209475 x 661211045 x 300555225 x 6011
Negative: -1 x -31407475-5 x -6281495-11 x -2855225-19 x -1653025-25 x -1256299-55 x -571045-95 x -330605-209 x -150275-275 x -114209-475 x -66121-1045 x -30055-5225 x -6011


How do I find the factor combinations of the number 31,407,475?

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 31,407,475, 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 31,407,475
-1 -31,407,475

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 31,407,475.

Example:
1 x 31,407,475 = 31,407,475
and
-1 x -31,407,475 = 31,407,475
Notice both answers equal 31,407,475

With that explanation out of the way, let's continue. Next, we take the number 31,407,475 and divide it by 2:

31,407,475 ÷ 2 = 15,703,737.5

If the quotient is a whole number, then 2 and 15,703,737.5 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 31,407,475
-1 -31,407,475

Now, we try dividing 31,407,475 by 3:

31,407,475 ÷ 3 = 10,469,158.3333

If the quotient is a whole number, then 3 and 10,469,158.3333 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 31,407,475
-1 -31,407,475

Let's try dividing by 4:

31,407,475 ÷ 4 = 7,851,868.75

If the quotient is a whole number, then 4 and 7,851,868.75 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 31,407,475
-1 31,407,475
Keep dividing by the next highest number until you cannot divide anymore.

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

1511192555952092754751,0455,2256,01130,05566,121114,209150,275330,605571,0451,256,2991,653,0252,855,2256,281,49531,407,475
-1-5-11-19-25-55-95-209-275-475-1,045-5,225-6,011-30,055-66,121-114,209-150,275-330,605-571,045-1,256,299-1,653,025-2,855,225-6,281,495-31,407,475

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