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
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
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.