Q: What are the factor combinations of the number 712,451,016?

 A:
Positive:   1 x 7124510162 x 3562255083 x 2374836724 x 1781127546 x 1187418368 x 890563779 x 7916122412 x 5937091818 x 3958061224 x 2968545936 x 1979030653 x 1344247272 x 9895153106 x 6721236159 x 4480824212 x 3360618318 x 2240412424 x 1680309477 x 1493608636 x 1120206954 x 7468041272 x 5601031908 x 3734023816 x 186701
Negative: -1 x -712451016-2 x -356225508-3 x -237483672-4 x -178112754-6 x -118741836-8 x -89056377-9 x -79161224-12 x -59370918-18 x -39580612-24 x -29685459-36 x -19790306-53 x -13442472-72 x -9895153-106 x -6721236-159 x -4480824-212 x -3360618-318 x -2240412-424 x -1680309-477 x -1493608-636 x -1120206-954 x -746804-1272 x -560103-1908 x -373402-3816 x -186701


How do I find the factor combinations of the number 712,451,016?

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 712,451,016, 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.

1 712,451,016
-1 -712,451,016

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 712,451,016.

Example:
1 x 712,451,016 = 712,451,016
and
-1 x -712,451,016 = 712,451,016
Notice both answers equal 712,451,016

With that explanation out of the way, let's continue. Next, we take the number 712,451,016 and divide it by 2:

712,451,016 ÷ 2 = 356,225,508

If the quotient is a whole number, then 2 and 356,225,508 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 356,225,508 712,451,016
-1 -2 -356,225,508 -712,451,016

Now, we try dividing 712,451,016 by 3:

712,451,016 ÷ 3 = 237,483,672

If the quotient is a whole number, then 3 and 237,483,672 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 237,483,672 356,225,508 712,451,016
-1 -2 -3 -237,483,672 -356,225,508 -712,451,016

Let's try dividing by 4:

712,451,016 ÷ 4 = 178,112,754

If the quotient is a whole number, then 4 and 178,112,754 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 178,112,754 237,483,672 356,225,508 712,451,016
-1 -2 -3 -4 -178,112,754 -237,483,672 -356,225,508 712,451,016
Keep dividing by the next highest number until you cannot divide anymore.

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

12346891218243653721061592123184244776369541,2721,9083,816186,701373,402560,103746,8041,120,2061,493,6081,680,3092,240,4123,360,6184,480,8246,721,2369,895,15313,442,47219,790,30629,685,45939,580,61259,370,91879,161,22489,056,377118,741,836178,112,754237,483,672356,225,508712,451,016
-1-2-3-4-6-8-9-12-18-24-36-53-72-106-159-212-318-424-477-636-954-1,272-1,908-3,816-186,701-373,402-560,103-746,804-1,120,206-1,493,608-1,680,309-2,240,412-3,360,618-4,480,824-6,721,236-9,895,153-13,442,472-19,790,306-29,685,459-39,580,612-59,370,918-79,161,224-89,056,377-118,741,836-178,112,754-237,483,672-356,225,508-712,451,016

More Examples

Here are some more numbers to try:

712,451,014712,451,015712,451,017712,451,018
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