36 = ___ x ___ x ____ x _____ or x 27 = ___ x ___ x ____ or
Find the prime factorization:
for example
36 = 2*18 =2*2*9 = 2*2*3*3
what is 3*3*3 ?
To find the prime factorization of a number, we need to break it down into its prime factors. We can do this by repeatedly dividing the number by prime numbers until we cannot divide it any further.
Let's start with the first equation:
36 = ___ x ___ x ____ x _____
Step 1: Start dividing the number by the smallest prime number, which is 2.
36 ÷ 2 = 18
Step 2: Continue dividing the result by 2.
18 ÷ 2 = 9
Step 3: Now, we cannot divide 9 by 2, so let's try the next prime number, which is 3.
9 ÷ 3 = 3
Step 4: We have reached 3, which is a prime number, so we stop dividing.
So, the prime factorization of 36 is 2 x 2 x 3 x 3, or in exponent form: 2^2 x 3^2.
Now, let's move on to the second equation:
x 27 = ___ x ___ x ____
Step 1: Start dividing the number by the smallest prime number, which is 2.
27 ÷ 2 = Not divisible by 2
Step 2: Next, divide it by 3.
27 ÷ 3 = 9
Step 3: Continue dividing the result by 3.
9 ÷ 3 = 3
Step 4: We have reached 3, which is a prime number, so we stop dividing.
So, the prime factorization of 27 is 3 x 3 x 3, or in exponent form: 3^3.
Therefore, the prime factorization of the given equations are:
36 = 2^2 x 3^2
27 = 3^3