Express 3465 as a product of it's prime factors
3465 = 3 × 5 × 7 × 11 × 3
To express 3465 as a product of its prime factors, follow these steps:
Step 1: Find the smallest prime number that divides 3465 evenly. The smallest prime number is 3. Divide 3465 by 3 to get 1155.
Step 2: Repeat step 1 with the new number. The smallest prime number that divides 1155 evenly is 3. Divide 1155 by 3 to get 385.
Step 3: Repeat step 1 again. The smallest prime number that divides 385 evenly is 5. Divide 385 by 5 to get 77.
Step 4: Repeat step 1 with 77. The smallest prime number that divides 77 evenly is 7. Divide 77 by 7 to get 11.
Step 5: At this point, we have reached a prime number. The prime factorization of 3465 can be written as 3 x 3 x 5 x 7 x 11, or in exponential form: 3^2 x 5 x 7 x 11.
Therefore, the prime factorization of 3465 is 3^2 x 5 x 7 x 11.