Q: What are the factor combinations of the number 146,267,525?

 A:
Positive:   1 x 1462675255 x 2925350525 x 585070147 x 3112075235 x 622415281 x 520525443 x 3301751175 x 1244831405 x 1041052215 x 660357025 x 2082111075 x 13207
Negative: -1 x -146267525-5 x -29253505-25 x -5850701-47 x -3112075-235 x -622415-281 x -520525-443 x -330175-1175 x -124483-1405 x -104105-2215 x -66035-7025 x -20821-11075 x -13207


How do I find the factor combinations of the number 146,267,525?

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 146,267,525, 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.

1 146,267,525
-1 -146,267,525

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 146,267,525.

Example:
1 x 146,267,525 = 146,267,525
and
-1 x -146,267,525 = 146,267,525
Notice both answers equal 146,267,525

With that explanation out of the way, let's continue. Next, we take the number 146,267,525 and divide it by 2:

146,267,525 ÷ 2 = 73,133,762.5

If the quotient is a whole number, then 2 and 73,133,762.5 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:

1 146,267,525
-1 -146,267,525

Now, we try dividing 146,267,525 by 3:

146,267,525 ÷ 3 = 48,755,841.6667

If the quotient is a whole number, then 3 and 48,755,841.6667 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:

1 146,267,525
-1 -146,267,525

Let's try dividing by 4:

146,267,525 ÷ 4 = 36,566,881.25

If the quotient is a whole number, then 4 and 36,566,881.25 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:

1 146,267,525
-1 146,267,525
Keep dividing by the next highest number until you cannot divide anymore.

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

1525472352814431,1751,4052,2157,02511,07513,20720,82166,035104,105124,483330,175520,525622,4153,112,0755,850,70129,253,505146,267,525
-1-5-25-47-235-281-443-1,175-1,405-2,215-7,025-11,075-13,207-20,821-66,035-104,105-124,483-330,175-520,525-622,415-3,112,075-5,850,701-29,253,505-146,267,525

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