Q: What are the factor combinations of the number 144,610,153?

 A:
Positive:   1 x 14461015329 x 498655773 x 198096183 x 1742291823 x 1757112117 x 683092407 x 600796059 x 23867
Negative: -1 x -144610153-29 x -4986557-73 x -1980961-83 x -1742291-823 x -175711-2117 x -68309-2407 x -60079-6059 x -23867


How do I find the factor combinations of the number 144,610,153?

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 144,610,153, 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.

1 144,610,153
-1 -144,610,153

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 144,610,153.

Example:
1 x 144,610,153 = 144,610,153
and
-1 x -144,610,153 = 144,610,153
Notice both answers equal 144,610,153

With that explanation out of the way, let's continue. Next, we take the number 144,610,153 and divide it by 2:

144,610,153 ÷ 2 = 72,305,076.5

If the quotient is a whole number, then 2 and 72,305,076.5 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:

1 144,610,153
-1 -144,610,153

Now, we try dividing 144,610,153 by 3:

144,610,153 ÷ 3 = 48,203,384.3333

If the quotient is a whole number, then 3 and 48,203,384.3333 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:

1 144,610,153
-1 -144,610,153

Let's try dividing by 4:

144,610,153 ÷ 4 = 36,152,538.25

If the quotient is a whole number, then 4 and 36,152,538.25 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:

1 144,610,153
-1 144,610,153
Keep dividing by the next highest number until you cannot divide anymore.

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

12973838232,1172,4076,05923,86760,07968,309175,7111,742,2911,980,9614,986,557144,610,153
-1-29-73-83-823-2,117-2,407-6,059-23,867-60,079-68,309-175,711-1,742,291-1,980,961-4,986,557-144,610,153

More Examples

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