What is the prime factorization of 540?
Can you help me?
start with 2 and work your way up
540 / 2 = 270
270 / 2 = 135
135 / 3 = 45
45 / 3 = 15
15 / 3 = 5 , which is prime
2^2 * 3^3 * 5
Of course! I can help you with finding the prime factorization of 540. To find the prime factorization, we need to decompose the number into its prime factors.
Step 1: Divide 540 by the smallest prime number, which is 2. We continue dividing by 2 until we can no longer divide evenly. In this case, 540 divided by 2 equals 270.
Step 2: We repeat the process with the quotient obtained in the previous step. Divide 270 by 2 again, and we get 135.
Step 3: Again, divide 135 by 2, which gives us 67.5. However, 67.5 is not a whole number, so we move on to the next prime number.
Step 4: Now, we try dividing 135 by the next prime number, which is 3. 135 divided by 3 equals 45.
Step 5: Divide 45 by 3, and we get 15.
Step 6: Divide 15 by 3 once again, which leaves us with 5.
Step 7: Finally, we divide 5 by the next prime number, which is 5 itself. And we are left with 1.
Now, let's summarize the results: The prime factorization of 540 is 2 × 2 × 3 × 3 × 3 × 5, or in exponential form, 2^2 × 3^3 × 5.
. . . . . . . . . . . . . . . . . . 540
. . . . . . . . . . . . . . . . . / . . . \
. . . . . . . . . . . . . . . 10 . . . . . 54
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