Answer: 3^3 × 5 × 13
Step-by-step explanation:
The prime factorization of 1755 is the expression of 1755 as the product of its prime factors. To find the prime factorization of 1755, we can iteratively divide 1755 by the smallest prime number possible until the result equals 1. The smallest prime number which can divide 1755 without a remainder is 3. So the first calculation step would look like this.
1755 ÷ 3 = 585
Now we repeat this action until the result equals 1
585 ÷ 3 = 195
195 ÷ 3 = 65
65 ÷ 5 = 13
13 ÷ 13 = 1
Therefore, the prime factors of 1755 are 3, 3, 3, 5, and 13. We can express the prime factorization of 1755 in exponential form as
1755 = 3^3 × 5 × 13
Therefore, the prime factorization of 1755 is 3^3 × 5 × 13
