Give the prime factorization of each of the following numbers :
420

Answer

To find the prime factorization of the number 420, we will break it down into its prime factors step by step.

### Step-by-Step Solution:

1. **Start with the number 420.**
- We will divide it by the smallest prime number, which is 2.

2. **Divide 420 by 2:**
- \( 420 \div 2 = 210 \)
- So, 2 is a prime factor.

3. **Divide 210 by 2 again:**
- \( 210 \div 2 = 105 \)
- We have another 2 as a prime factor.

4. **Now, divide 105 by the next smallest prime number, which is 3:**
- \( 105 \div 3 = 35 \)
- So, 3 is a prime factor.

5. **Next, divide 35 by the next smallest prime number, which is 5:**
- \( 35 \div 5 = 7 \)
- So, 5 is a prime factor.

6. **Finally, we are left with 7, which is also a prime number:**
- \( 7 \div 7 = 1 \)
- So, 7 is a prime factor.

7. **Now, we can write the prime factorization of 420:**
- We have used two 2's, one 3, one 5, and one 7.
- Therefore, the prime factorization of 420 is:
\[ 2^2 \times 3^1 \times 5^1 \times 7^1 \]

### Final Answer:
The prime factorization of 420 is \( 2^2 \times 3^1 \times 5^1 \times 7^1 \).

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