Express 5400 as the product of its prime factors
To express 5400 as the product of its prime factors, we need to find all the prime numbers that divide evenly into 5400.
First, we divide 5400 by 2:
5400 ÷ 2 = 2700
Now, we divide 2700 by 2:
2700 ÷ 2 = 1350
Next, we divide 1350 by 2 again:
1350 ÷ 2 = 675
At this point, we can no longer divide by 2 because it is an odd number. So, we move on to the next prime number, which is 3:
675 ÷ 3 = 225
Now, we divide 225 by 3 again:
225 ÷ 3 = 75
Again, we divide 75 by 3:
75 ÷ 3 = 25
Now, we divide 25 by 5, another prime number:
25 ÷ 5 = 5
Finally, we divide 5 by itself:
5 ÷ 5 = 1
Therefore, the prime factorization of 5400 is:
2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 = 2^3 × 3^3 × 5^2
To express 5400 as the product of its prime factors, we can follow these steps:
Step 1: Start with the number and the smallest prime number, which is 2.
5400 ÷ 2 = 2700
Step 2: Continue to divide by 2 until it is no longer possible.
2700 ÷ 2 = 1350
1350 ÷ 2 = 675
Step 3: Move on to the next prime number, which is 3.
675 ÷ 3 = 225
Step 4: Continue to divide by 3 until it is no longer possible.
225 ÷ 3 = 75
75 ÷ 3 = 25
Step 5: Now, divide by the next prime number, 5.
25 ÷ 5 = 5
Step 6: Finally, divide by the last prime number, 5, again.
5 ÷ 5 = 1
Now, we have found the prime factorization of 5400:
5400 = 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5
To express 5400 as the product of its prime factors, we need to find all the prime numbers that, when multiplied together, give us the original number.
The first step is to divide the number by the smallest prime number, which is 2. If the number is divisible by 2, we continue dividing by 2 until it is no longer divisible.
5400 ÷ 2 = 2700
2700 ÷ 2 = 1350
1350 ÷ 2 = 675
675 ÷ 3 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
Now, let's list all the prime factors we used:
2, 2, 2, 3, 3, 5
Therefore, the prime factors of 5400 are 2, 2, 2, 3, 3, and 5. We can express 5400 as the product of its prime factors like this:
5400 = 2 × 2 × 2 × 3 × 3 × 5