wHAT ARE THE PRIME FACTORARIZATON OF 180?
Recall that a prime number can not be divided evenly by any number except itself and 1.
The first several primes are 2, 3, and 5.
try 2
180/2 = 90
180/2 = 45
45 is not evenly divisible by 2.
try 3
45/3 = 15
15/3 = 5
5 is a prime. So now the prime factorization is:
5 * 3 * 3 * 2 * 2 = 180
I will start you .
Start with the lowest prime: 2
2*90
Now start with another 2
2*2*45
You cant do another 2, so go up: 3 can be used, so
2*2*3*? and keep proceeding...
To find the prime factorization of 180, we need to find its prime factors, which are the prime numbers that can divide 180 evenly.
Here's how you can do it:
Step 1: Start by dividing 180 by the smallest prime number, which is 2. If 2 divides evenly, it becomes one of the prime factors.
180 ÷ 2 = 90
Step 2: Repeat the process with the result from the previous step. Divide 90 by 2 again.
90 ÷ 2 = 45
Step 3: Keep repeating the division process until you can no longer divide evenly by 2.
45 ÷ 3 = 15
Step 4: Now, try dividing 15 by the next smallest prime number, which is 3.
15 ÷ 3 = 5
Step 5: Finally, try dividing 5 by the next smallest prime number, which is also 5.
5 ÷ 5 = 1
Step 6: Once you reach 1, you stop because all the prime factors have been found.
The prime factors of 180 are 2, 2, 3, 3, and 5.
Therefore, the prime factorization of 180 is 2² × 3² × 5.