Find the prime factorization of 540
bad
very dirty bad
To find the prime factorization of 540, we need to determine the prime numbers that multiply together to give 540. Here's a step-by-step process to find the prime factorization:
1. Start by dividing 540 by the smallest prime number, which is 2. Since 540 is an even number, it is divisible by 2. Divide 540 by 2 to get 270.
- 540 ÷ 2 = 270
2. Next, we continue to divide the quotient (which is 270) by 2 until it is no longer divisible by 2. Divide 270 by 2 to get 135.
- 270 ÷ 2 = 135
3. Now we move on to the next prime number, which is 3. Divide 135 by 3 to get 45.
- 135 ÷ 3 = 45
4. Continuing with the next prime factor, we divide 45 by 3 again to get 15.
- 45 ÷ 3 = 15
5. Now, we divide 15 by the next prime number, which is 5. It divides evenly, resulting in 3.
- 15 ÷ 5 = 3
6. Finally, we divide 3 by itself, as it is a prime number.
- 3 ÷ 3 = 1
We have reached the end of the prime factorization process when we obtain a quotient of 1. Now, we can write down the prime factors of 540:
2 × 2 × 3 × 3 × 3 × 5 = 2² × 3³ × 5
Therefore, the prime factorization of 540 is 2² × 3³ × 5.
start with the smaller factors
540 = 2*270
=2*2*125
= 2*2*3*45
= 2*2*3*3*15
= 2*2*3*3*3*5
or 2^2 * 3^3 * 5