Give the prime factorzation of 20570.

Answer

To find the prime factorization of 20570, we will break it down step by step.

### Step 1: Start with the number 20570
We need to find the prime factors of 20570.

### Step 2: Divide by the smallest prime number
The smallest prime number is 2. Since 20570 is even, we can divide it by 2.

\[ 20570 \div 2 = 10285 \]

### Step 3: Check if the result is divisible by 5
Next, we check if 10285 is divisible by 5 (the next smallest prime). Since it ends with a 5, we can divide it by 5.

\[ 10285 \div 5 = 2057 \]

### Step 4: Check for divisibility by 11
Now we need to factor 2057. We can check for divisibility by 11.

\[ 2057 \div 11 = 187 \]

### Step 5: Continue factoring 187
Next, we factor 187. We can divide it by 11 again.

\[ 187 \div 11 = 17 \]

### Step 6: Factor 17
Now we have 17, which is a prime number.

\[ 17 \div 17 = 1 \]

### Step 7: Compile the prime factors
Now we can compile all the prime factors we found:

- From step 2: 2
- From step 3: 5
- From steps 4 and 5: 11 (which we found twice)
- From step 6: 17

Thus, the prime factorization of 20570 is:

\[ 2 \times 5 \times 11^2 \times 17 \]

### Final Answer
The prime factorization of 20570 is \( 2 \times 5 \times 11^2 \times 17 \).

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