Express 3135 as a product of its prime numbers.
The prime factorization of 3135 is:
3135 = 3 × 3 × 5 × 7 × 5
To express 3135 as a product of its prime numbers, we need to find the prime factorization of 3135.
First, we divide 3135 by the smallest prime number, which is 2. However, 3135 is an odd number, so it is not divisible by 2.
Next, we try with the next smallest prime number, which is 3. We divide 3135 by 3. The result is 1045, with no remainder.
Now, we continue dividing 1045 by the smallest prime numbers until we cannot divide further:
1045 ÷ 3 = 348.33 (not divisible by 3)
348 ÷ 2 = 174
174 ÷ 2 = 87
87 ÷ 3 = 29
At this stage, we cannot continue dividing further as 29 is a prime number.
Therefore, the prime factorization of 3135 is: 3 * 3 * 5 * 29, or written as a product: 3^2 * 5 * 29.
To express 3135 as a product of its prime numbers, we need to find all the prime factors of 3135.
Let's start by dividing 3135 by the smallest prime number, which is 2:
3135 ÷ 2 = 1567.5
Since 1567.5 is not a whole number, we can conclude that 2 is not a factor of 3135.
Now, let's try the next prime number, which is 3:
3135 ÷ 3 = 1045
Again, 1045 is not divisible by 3, so 3 is also not a factor of 3135.
Moving on to the next prime number, which is 5:
3135 ÷ 5 = 627
This time, 627 is divisible by 5:
627 ÷ 5 = 125.4
We can see that 5 is a factor of 3135.
Now, let's continue factoring 627. We start by dividing it by 3:
627 ÷ 3 = 209
209 is not divisible by 3 or 5, so we move on to the next prime number, which is 7:
209 ÷ 7 = 29.857142857142857
Again, 7 is not a factor of 209.
Finally, let's try 11 as a divisor:
209 ÷ 11 = 19
Now, we have found another prime factor of 3135, which is 11.
At this point, 3135 has been fully factored into its prime factors: 5, 11, and 19.
So, the prime factorization of 3135 is:
3135 = 5 × 11 × 19