what is the prime factorization of 420
420 = 2*2*3*5*7
2*2*3*5*7
To determine the prime factorization of 420, we need to find all the prime numbers that can divide evenly into it.
Step 1: Start by dividing 420 by the smallest prime number, which is 2. 420 ÷ 2 = 210.
Step 2: Now, divide the result, 210, by 2 again. 210 ÷ 2 = 105.
Step 3: Repeat the process with the new result, dividing 105 by 2. However, 105 is not divisible by 2.
Step 4: Move on to the next prime number, which is 3. Divide 105 by 3. 105 ÷ 3 = 35.
Step 5: The next prime number is 5. Divide 35 by 5. 35 ÷ 5 = 7.
At this point, we have reached 7, which is a prime number. We stop here because prime numbers have no other divisors. Therefore, the prime factorization of 420 is 2 × 2 × 3 × 5 × 7, or written in exponential form as 2^2 × 3 × 5 × 7.