Find the greatest common factor of 270 and 360. (Give the answer in the numerical form in the top box and in exponential form by filling in the boxes for exponents.)

270 = 2 * 3^3 * 5

360 = 2^3 * 3^2 * 5

Now pick the factors with the highest power of each prime, common to both numbers:

GCF = 2 * 3^2 * 5 = 90

Well, finding the greatest common factor is a bit like finding the common bond between two celebrities. In this case, let's find the GCF of 270 and 360.

Step right up, folks! In the left corner, we have 270. And in the right corner, we have 360.

Now, let's see what these two numbers have in common. Both 270 and 360 can be divided by 2 and 3. But wait, there's more! 270 can also be divided by 5, while 360 can also be divided by 2 (again) and 5.

So, what is the greatest common factor, you ask? It's none other than 2 times 5, which gives us... (drumroll, please)... 10!

In numerical form, the greatest common factor is 10. In exponential form, we can write it as 2^1 * 5^1.

To find the greatest common factor (GCF) of 270 and 360, we can prime factorize both numbers and identify the common prime factors.

Prime factorization of 270:
270 = 2 * 3 * 3 * 3 * 5
270 = 2^1 * 3^3 * 5^1

Prime factorization of 360:
360 = 2 * 2 * 2 * 3 * 3 * 5
360 = 2^3 * 3^2 * 5^1

To find the GCF, we multiply the common prime factors with their lowest exponent:
GCF = 2^1 * 3^2 * 5^1

In the numerical form, the GCF of 270 and 360 is 30.
In exponential form:
GCF = 2^1 * 3^2 * 5^1

To find the greatest common factor (GCF) of 270 and 360, we need to find the largest number that divides evenly into both numbers.

First, let's list the prime factors of each number.
270:
- 2 x 135
- 2 x 3 x 45
- 2 x 3 x 3 x 15
- 2 x 3 x 3 x 3 x 5

360:
- 2 x 180
- 2 x 2 x 90
- 2 x 2 x 2 x 45
- 2 x 2 x 2 x 3 x 15
- 2 x 2 x 2 x 3 x 3 x 5

Now, let's identify the common prime factors between the two lists:
- 2 x 3 x 3 x 5

Finally, we multiply the common prime factors together to find the GCF:
2 x 3 x 3 x 5 = 90

Therefore, the greatest common factor of 270 and 360 is 90.

In exponential form:
GCF = 2^1 x 3^2 x 5^1