Q: What are the factor combinations of the number 34,122,420?

 A:
Positive:   1 x 341224202 x 170612103 x 113741404 x 85306055 x 68244846 x 56870709 x 379138010 x 341224212 x 284353515 x 227482818 x 189569020 x 170612130 x 113741436 x 94784545 x 75827660 x 56870790 x 379138163 x 209340180 x 189569326 x 104670489 x 69780652 x 52335815 x 41868978 x 348901163 x 293401467 x 232601630 x 209341956 x 174452326 x 146702445 x 139562934 x 116303260 x 104673489 x 97804652 x 73354890 x 69785815 x 5868
Negative: -1 x -34122420-2 x -17061210-3 x -11374140-4 x -8530605-5 x -6824484-6 x -5687070-9 x -3791380-10 x -3412242-12 x -2843535-15 x -2274828-18 x -1895690-20 x -1706121-30 x -1137414-36 x -947845-45 x -758276-60 x -568707-90 x -379138-163 x -209340-180 x -189569-326 x -104670-489 x -69780-652 x -52335-815 x -41868-978 x -34890-1163 x -29340-1467 x -23260-1630 x -20934-1956 x -17445-2326 x -14670-2445 x -13956-2934 x -11630-3260 x -10467-3489 x -9780-4652 x -7335-4890 x -6978-5815 x -5868


How do I find the factor combinations of the number 34,122,420?

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 34,122,420, 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 34,122,420
-1 -34,122,420

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 34,122,420.

Example:
1 x 34,122,420 = 34,122,420
and
-1 x -34,122,420 = 34,122,420
Notice both answers equal 34,122,420

With that explanation out of the way, let's continue. Next, we take the number 34,122,420 and divide it by 2:

34,122,420 ÷ 2 = 17,061,210

If the quotient is a whole number, then 2 and 17,061,210 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 17,061,210 34,122,420
-1 -2 -17,061,210 -34,122,420

Now, we try dividing 34,122,420 by 3:

34,122,420 ÷ 3 = 11,374,140

If the quotient is a whole number, then 3 and 11,374,140 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 11,374,140 17,061,210 34,122,420
-1 -2 -3 -11,374,140 -17,061,210 -34,122,420

Let's try dividing by 4:

34,122,420 ÷ 4 = 8,530,605

If the quotient is a whole number, then 4 and 8,530,605 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 8,530,605 11,374,140 17,061,210 34,122,420
-1 -2 -3 -4 -8,530,605 -11,374,140 -17,061,210 34,122,420
Keep dividing by the next highest number until you cannot divide anymore.

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

1234569101215182030364560901631803264896528159781,1631,4671,6301,9562,3262,4452,9343,2603,4894,6524,8905,8155,8686,9787,3359,78010,46711,63013,95614,67017,44520,93423,26029,34034,89041,86852,33569,780104,670189,569209,340379,138568,707758,276947,8451,137,4141,706,1211,895,6902,274,8282,843,5353,412,2423,791,3805,687,0706,824,4848,530,60511,374,14017,061,21034,122,420
-1-2-3-4-5-6-9-10-12-15-18-20-30-36-45-60-90-163-180-326-489-652-815-978-1,163-1,467-1,630-1,956-2,326-2,445-2,934-3,260-3,489-4,652-4,890-5,815-5,868-6,978-7,335-9,780-10,467-11,630-13,956-14,670-17,445-20,934-23,260-29,340-34,890-41,868-52,335-69,780-104,670-189,569-209,340-379,138-568,707-758,276-947,845-1,137,414-1,706,121-1,895,690-2,274,828-2,843,535-3,412,242-3,791,380-5,687,070-6,824,484-8,530,605-11,374,140-17,061,210-34,122,420

More Examples

Here are some more numbers to try:

34,122,41834,122,41934,122,42134,122,422
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