Q: What are the factor combinations of the number 43,743,648?

 A:
Positive:   1 x 437436482 x 218718243 x 145812164 x 109359126 x 72906088 x 546795612 x 364530413 x 336489616 x 273397824 x 182265226 x 168244832 x 136698939 x 112163248 x 91132652 x 84122478 x 56081696 x 455663104 x 420612156 x 280408208 x 210306312 x 140204416 x 105153624 x 701021248 x 35051
Negative: -1 x -43743648-2 x -21871824-3 x -14581216-4 x -10935912-6 x -7290608-8 x -5467956-12 x -3645304-13 x -3364896-16 x -2733978-24 x -1822652-26 x -1682448-32 x -1366989-39 x -1121632-48 x -911326-52 x -841224-78 x -560816-96 x -455663-104 x -420612-156 x -280408-208 x -210306-312 x -140204-416 x -105153-624 x -70102-1248 x -35051


How do I find the factor combinations of the number 43,743,648?

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 43,743,648, 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 43,743,648
-1 -43,743,648

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 43,743,648.

Example:
1 x 43,743,648 = 43,743,648
and
-1 x -43,743,648 = 43,743,648
Notice both answers equal 43,743,648

With that explanation out of the way, let's continue. Next, we take the number 43,743,648 and divide it by 2:

43,743,648 ÷ 2 = 21,871,824

If the quotient is a whole number, then 2 and 21,871,824 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 21,871,824 43,743,648
-1 -2 -21,871,824 -43,743,648

Now, we try dividing 43,743,648 by 3:

43,743,648 ÷ 3 = 14,581,216

If the quotient is a whole number, then 3 and 14,581,216 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 14,581,216 21,871,824 43,743,648
-1 -2 -3 -14,581,216 -21,871,824 -43,743,648

Let's try dividing by 4:

43,743,648 ÷ 4 = 10,935,912

If the quotient is a whole number, then 4 and 10,935,912 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 10,935,912 14,581,216 21,871,824 43,743,648
-1 -2 -3 -4 -10,935,912 -14,581,216 -21,871,824 43,743,648
Keep dividing by the next highest number until you cannot divide anymore.

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

12346812131624263239485278961041562083124166241,24835,05170,102105,153140,204210,306280,408420,612455,663560,816841,224911,3261,121,6321,366,9891,682,4481,822,6522,733,9783,364,8963,645,3045,467,9567,290,60810,935,91214,581,21621,871,82443,743,648
-1-2-3-4-6-8-12-13-16-24-26-32-39-48-52-78-96-104-156-208-312-416-624-1,248-35,051-70,102-105,153-140,204-210,306-280,408-420,612-455,663-560,816-841,224-911,326-1,121,632-1,366,989-1,682,448-1,822,652-2,733,978-3,364,896-3,645,304-5,467,956-7,290,608-10,935,912-14,581,216-21,871,824-43,743,648

More Examples

Here are some more numbers to try:

43,743,64643,743,64743,743,64943,743,650
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