Q: What are the factor combinations of the number 150,235,525?

 A:
Positive:   1 x 1502355255 x 3004710511 x 1365777525 x 600942155 x 2731555275 x 546311659 x 227975829 x 1812253295 x 455954145 x 362457249 x 207259119 x 16475
Negative: -1 x -150235525-5 x -30047105-11 x -13657775-25 x -6009421-55 x -2731555-275 x -546311-659 x -227975-829 x -181225-3295 x -45595-4145 x -36245-7249 x -20725-9119 x -16475


How do I find the factor combinations of the number 150,235,525?

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 150,235,525, 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.

1 150,235,525
-1 -150,235,525

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 150,235,525.

Example:
1 x 150,235,525 = 150,235,525
and
-1 x -150,235,525 = 150,235,525
Notice both answers equal 150,235,525

With that explanation out of the way, let's continue. Next, we take the number 150,235,525 and divide it by 2:

150,235,525 ÷ 2 = 75,117,762.5

If the quotient is a whole number, then 2 and 75,117,762.5 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:

1 150,235,525
-1 -150,235,525

Now, we try dividing 150,235,525 by 3:

150,235,525 ÷ 3 = 50,078,508.3333

If the quotient is a whole number, then 3 and 50,078,508.3333 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:

1 150,235,525
-1 -150,235,525

Let's try dividing by 4:

150,235,525 ÷ 4 = 37,558,881.25

If the quotient is a whole number, then 4 and 37,558,881.25 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:

1 150,235,525
-1 150,235,525
Keep dividing by the next highest number until you cannot divide anymore.

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

151125552756598293,2954,1457,2499,11916,47520,72536,24545,595181,225227,975546,3112,731,5556,009,42113,657,77530,047,105150,235,525
-1-5-11-25-55-275-659-829-3,295-4,145-7,249-9,119-16,475-20,725-36,245-45,595-181,225-227,975-546,311-2,731,555-6,009,421-13,657,775-30,047,105-150,235,525

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