2x3x5x8x11=
with a 2 on top of 2 and a 4 on top of 5 and 2 on top of 11
is this a factorization a prime factorization
Huh??
you mean (2^2)(3)(5^4)(11^2) ?
If so, then yes, it is fully factored in prime notation.
To find the prime factorization of 2x3x5x8x11, we need to break down each number into its prime factors.
Let's start with 2: 2 can only be divided by itself, so its prime factorization is simply 2.
Next, 3 is already a prime number, so its prime factorization is 3 itself.
Moving on to 5: 5 is also a prime number, so its prime factorization is only 5.
Now, let's factorize 8: 8 can be divided by 2 three times, so its prime factorization is 2x2x2, which can be written as 2^3.
Finally, 11 is a prime number, so its prime factorization is 11 itself.
To find the prime factorization of the entire expression, we simply multiply the prime factors of each number together:
2x3x5x8x11 = (2)(3)(5)(2^3)(11)
Writing it in exponential form:
= 2^4 x 3 x 5 x 11
So, the prime factorization of 2x3x5x8x11 is 2^4 x 3 x 5 x 11.
To find the value of 2x3x5x8x11, we first need to multiply all the numbers together. Let's break it down step by step:
1. Multiply 2 and 3: 2 x 3 = 6
2. Multiply the result from step 1 by 5: 6 x 5 = 30
3. Multiply the result from step 2 by 8: 30 x 8 = 240
4. Multiply the result from step 3 by 11: 240 x 11 = 2640
So, 2x3x5x8x11 = 2640.
Now let's discuss the "factorization" and "prime factorization" part.
Factorization refers to expressing a number as a product of its factors. In this case, 2640 can be factored as the product of 2, 3, 5, 8, and 11.
Prime factorization, on the other hand, is when we write a number as a product of its prime factors. Prime factors are prime numbers that can divide a given number without leaving any remainder.
To find the prime factorization of 2640, we can start by dividing it by the smallest prime number, which is 2:
2640 ÷ 2 = 1320
Now, we continue dividing the quotient (1320) by 2:
1320 ÷ 2 = 660
We can see that 660 is also divisible by 2:
660 ÷ 2 = 330
And 330 is divisible by 2 as well:
330 ÷ 2 = 165
Now, 165 is divisible by 3:
165 ÷ 3 = 55
Lastly, 55 is divisible by 5:
55 ÷ 5 = 11
Now we have reached a prime number (11), and there are no other prime factors left. Thus, the prime factorization of 2640 is:
2 x 2 x 2 x 3 x 5 x 11
This means that 2x3x5x8x11 is not just a factorization but also the prime factorization of 2640.