Q: What are the factor combinations of the number 27,742,464?

 A:
Positive:   1 x 277424642 x 138712323 x 92474884 x 69356166 x 46237448 x 34678089 x 308249612 x 231187216 x 173390418 x 154124824 x 115593632 x 86695236 x 77062448 x 57796864 x 43347672 x 38531296 x 288984128 x 216738144 x 192656192 x 144492256 x 108369288 x 96328384 x 72246576 x 48164768 x 361231152 x 240822304 x 12041
Negative: -1 x -27742464-2 x -13871232-3 x -9247488-4 x -6935616-6 x -4623744-8 x -3467808-9 x -3082496-12 x -2311872-16 x -1733904-18 x -1541248-24 x -1155936-32 x -866952-36 x -770624-48 x -577968-64 x -433476-72 x -385312-96 x -288984-128 x -216738-144 x -192656-192 x -144492-256 x -108369-288 x -96328-384 x -72246-576 x -48164-768 x -36123-1152 x -24082-2304 x -12041


How do I find the factor combinations of the number 27,742,464?

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 27,742,464, 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 27,742,464
-1 -27,742,464

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 27,742,464.

Example:
1 x 27,742,464 = 27,742,464
and
-1 x -27,742,464 = 27,742,464
Notice both answers equal 27,742,464

With that explanation out of the way, let's continue. Next, we take the number 27,742,464 and divide it by 2:

27,742,464 ÷ 2 = 13,871,232

If the quotient is a whole number, then 2 and 13,871,232 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 13,871,232 27,742,464
-1 -2 -13,871,232 -27,742,464

Now, we try dividing 27,742,464 by 3:

27,742,464 ÷ 3 = 9,247,488

If the quotient is a whole number, then 3 and 9,247,488 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 9,247,488 13,871,232 27,742,464
-1 -2 -3 -9,247,488 -13,871,232 -27,742,464

Let's try dividing by 4:

27,742,464 ÷ 4 = 6,935,616

If the quotient is a whole number, then 4 and 6,935,616 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 6,935,616 9,247,488 13,871,232 27,742,464
-1 -2 -3 -4 -6,935,616 -9,247,488 -13,871,232 27,742,464
Keep dividing by the next highest number until you cannot divide anymore.

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

1234689121618243236486472961281441922562883845767681,1522,30412,04124,08236,12348,16472,24696,328108,369144,492192,656216,738288,984385,312433,476577,968770,624866,9521,155,9361,541,2481,733,9042,311,8723,082,4963,467,8084,623,7446,935,6169,247,48813,871,23227,742,464
-1-2-3-4-6-8-9-12-16-18-24-32-36-48-64-72-96-128-144-192-256-288-384-576-768-1,152-2,304-12,041-24,082-36,123-48,164-72,246-96,328-108,369-144,492-192,656-216,738-288,984-385,312-433,476-577,968-770,624-866,952-1,155,936-1,541,248-1,733,904-2,311,872-3,082,496-3,467,808-4,623,744-6,935,616-9,247,488-13,871,232-27,742,464

More Examples

Here are some more numbers to try:

27,742,46227,742,46327,742,46527,742,466
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