Q: What are the factor combinations of the number 742,403,460?

 A:
Positive:   1 x 7424034602 x 3712017303 x 2474678204 x 1856008655 x 1484806926 x 12373391010 x 7424034612 x 6186695515 x 4949356420 x 3712017330 x 2474678260 x 1237339183 x 8944620166 x 4472310249 x 2981540332 x 2236155415 x 1788924498 x 1490770830 x 894462996 x 7453851245 x 5963081660 x 4472312490 x 2981544980 x 149077
Negative: -1 x -742403460-2 x -371201730-3 x -247467820-4 x -185600865-5 x -148480692-6 x -123733910-10 x -74240346-12 x -61866955-15 x -49493564-20 x -37120173-30 x -24746782-60 x -12373391-83 x -8944620-166 x -4472310-249 x -2981540-332 x -2236155-415 x -1788924-498 x -1490770-830 x -894462-996 x -745385-1245 x -596308-1660 x -447231-2490 x -298154-4980 x -149077


How do I find the factor combinations of the number 742,403,460?

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 742,403,460, 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.

1 742,403,460
-1 -742,403,460

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 742,403,460.

Example:
1 x 742,403,460 = 742,403,460
and
-1 x -742,403,460 = 742,403,460
Notice both answers equal 742,403,460

With that explanation out of the way, let's continue. Next, we take the number 742,403,460 and divide it by 2:

742,403,460 ÷ 2 = 371,201,730

If the quotient is a whole number, then 2 and 371,201,730 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 2 371,201,730 742,403,460
-1 -2 -371,201,730 -742,403,460

Now, we try dividing 742,403,460 by 3:

742,403,460 ÷ 3 = 247,467,820

If the quotient is a whole number, then 3 and 247,467,820 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 3 247,467,820 371,201,730 742,403,460
-1 -2 -3 -247,467,820 -371,201,730 -742,403,460

Let's try dividing by 4:

742,403,460 ÷ 4 = 185,600,865

If the quotient is a whole number, then 4 and 185,600,865 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 4 185,600,865 247,467,820 371,201,730 742,403,460
-1 -2 -3 -4 -185,600,865 -247,467,820 -371,201,730 742,403,460
Keep dividing by the next highest number until you cannot divide anymore.

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

123456101215203060831662493324154988309961,2451,6602,4904,980149,077298,154447,231596,308745,385894,4621,490,7701,788,9242,236,1552,981,5404,472,3108,944,62012,373,39124,746,78237,120,17349,493,56461,866,95574,240,346123,733,910148,480,692185,600,865247,467,820371,201,730742,403,460
-1-2-3-4-5-6-10-12-15-20-30-60-83-166-249-332-415-498-830-996-1,245-1,660-2,490-4,980-149,077-298,154-447,231-596,308-745,385-894,462-1,490,770-1,788,924-2,236,155-2,981,540-4,472,310-8,944,620-12,373,391-24,746,782-37,120,173-49,493,564-61,866,955-74,240,346-123,733,910-148,480,692-185,600,865-247,467,820-371,201,730-742,403,460

More Examples

Here are some more numbers to try:

742,403,458742,403,459742,403,461742,403,462
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