Q: What are the factor combinations of the number 421,505,532?

 A:
Positive:   1 x 4215055322 x 2107527663 x 1405018444 x 1053763836 x 702509227 x 602150769 x 4683394812 x 3512546114 x 3010753818 x 2341697421 x 2007169227 x 1561131628 x 1505376936 x 1170848742 x 1003584654 x 780565863 x 669056481 x 520377284 x 5017923108 x 3902829126 x 3345282162 x 2601886189 x 2230188252 x 1672641324 x 1300943378 x 1115094567 x 743396756 x 5575471134 x 3716982268 x 185849
Negative: -1 x -421505532-2 x -210752766-3 x -140501844-4 x -105376383-6 x -70250922-7 x -60215076-9 x -46833948-12 x -35125461-14 x -30107538-18 x -23416974-21 x -20071692-27 x -15611316-28 x -15053769-36 x -11708487-42 x -10035846-54 x -7805658-63 x -6690564-81 x -5203772-84 x -5017923-108 x -3902829-126 x -3345282-162 x -2601886-189 x -2230188-252 x -1672641-324 x -1300943-378 x -1115094-567 x -743396-756 x -557547-1134 x -371698-2268 x -185849


How do I find the factor combinations of the number 421,505,532?

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 421,505,532, 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.

1 421,505,532
-1 -421,505,532

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 421,505,532.

Example:
1 x 421,505,532 = 421,505,532
and
-1 x -421,505,532 = 421,505,532
Notice both answers equal 421,505,532

With that explanation out of the way, let's continue. Next, we take the number 421,505,532 and divide it by 2:

421,505,532 ÷ 2 = 210,752,766

If the quotient is a whole number, then 2 and 210,752,766 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 2 210,752,766 421,505,532
-1 -2 -210,752,766 -421,505,532

Now, we try dividing 421,505,532 by 3:

421,505,532 ÷ 3 = 140,501,844

If the quotient is a whole number, then 3 and 140,501,844 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 3 140,501,844 210,752,766 421,505,532
-1 -2 -3 -140,501,844 -210,752,766 -421,505,532

Let's try dividing by 4:

421,505,532 ÷ 4 = 105,376,383

If the quotient is a whole number, then 4 and 105,376,383 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 4 105,376,383 140,501,844 210,752,766 421,505,532
-1 -2 -3 -4 -105,376,383 -140,501,844 -210,752,766 421,505,532
Keep dividing by the next highest number until you cannot divide anymore.

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

12346791214182127283642546381841081261621892523243785677561,1342,268185,849371,698557,547743,3961,115,0941,300,9431,672,6412,230,1882,601,8863,345,2823,902,8295,017,9235,203,7726,690,5647,805,65810,035,84611,708,48715,053,76915,611,31620,071,69223,416,97430,107,53835,125,46146,833,94860,215,07670,250,922105,376,383140,501,844210,752,766421,505,532
-1-2-3-4-6-7-9-12-14-18-21-27-28-36-42-54-63-81-84-108-126-162-189-252-324-378-567-756-1,134-2,268-185,849-371,698-557,547-743,396-1,115,094-1,300,943-1,672,641-2,230,188-2,601,886-3,345,282-3,902,829-5,017,923-5,203,772-6,690,564-7,805,658-10,035,846-11,708,487-15,053,769-15,611,316-20,071,692-23,416,974-30,107,538-35,125,461-46,833,948-60,215,076-70,250,922-105,376,383-140,501,844-210,752,766-421,505,532

More Examples

Here are some more numbers to try:

421,505,530421,505,531421,505,533421,505,534
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