Q: What are the factor combinations of the number 21,000,175?

 A:
Positive:   1 x 210001755 x 42000357 x 300002525 x 84000731 x 67742535 x 60000549 x 42857579 x 265825155 x 135485175 x 120001217 x 96775245 x 85715343 x 61225395 x 53165553 x 37975775 x 270971085 x 193551225 x 171431519 x 138251715 x 122451975 x 106332449 x 85752765 x 75953871 x 5425
Negative: -1 x -21000175-5 x -4200035-7 x -3000025-25 x -840007-31 x -677425-35 x -600005-49 x -428575-79 x -265825-155 x -135485-175 x -120001-217 x -96775-245 x -85715-343 x -61225-395 x -53165-553 x -37975-775 x -27097-1085 x -19355-1225 x -17143-1519 x -13825-1715 x -12245-1975 x -10633-2449 x -8575-2765 x -7595-3871 x -5425


How do I find the factor combinations of the number 21,000,175?

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 21,000,175, 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 21,000,175
-1 -21,000,175

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 21,000,175.

Example:
1 x 21,000,175 = 21,000,175
and
-1 x -21,000,175 = 21,000,175
Notice both answers equal 21,000,175

With that explanation out of the way, let's continue. Next, we take the number 21,000,175 and divide it by 2:

21,000,175 ÷ 2 = 10,500,087.5

If the quotient is a whole number, then 2 and 10,500,087.5 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 21,000,175
-1 -21,000,175

Now, we try dividing 21,000,175 by 3:

21,000,175 ÷ 3 = 7,000,058.3333

If the quotient is a whole number, then 3 and 7,000,058.3333 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 21,000,175
-1 -21,000,175

Let's try dividing by 4:

21,000,175 ÷ 4 = 5,250,043.75

If the quotient is a whole number, then 4 and 5,250,043.75 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 21,000,175
-1 21,000,175
Keep dividing by the next highest number until you cannot divide anymore.

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

15725313549791551752172453433955537751,0851,2251,5191,7151,9752,4492,7653,8715,4257,5958,57510,63312,24513,82517,14319,35527,09737,97553,16561,22585,71596,775120,001135,485265,825428,575600,005677,425840,0073,000,0254,200,03521,000,175
-1-5-7-25-31-35-49-79-155-175-217-245-343-395-553-775-1,085-1,225-1,519-1,715-1,975-2,449-2,765-3,871-5,425-7,595-8,575-10,633-12,245-13,825-17,143-19,355-27,097-37,975-53,165-61,225-85,715-96,775-120,001-135,485-265,825-428,575-600,005-677,425-840,007-3,000,025-4,200,035-21,000,175

More Examples

Here are some more numbers to try:

21,000,17321,000,17421,000,17621,000,177
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