Answer:
420 = 2² × 3 × 5 × 7
Explanation:
The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, ...
To find which prime numbers multiply together to make 420, start by dividing 420 by the first prime number, 2:
⇒ 420 ÷ 2 = 210
As 210 is not a prime number, we need to divide again. Let's try dividing by 2 again:
⇒ 210 ÷ 2 = 105
As 105 is not a prime number, we need to divide again. 105 is not divisible by 2, so let's try dividing it by the next prime number, 3:
⇒ 105 ÷ 3 = 35
As 35 is not a prime number, we need to divide again. 35 is not divisible by 2 or 3, so let's try dividing it by the next prime number, 5:
⇒ 35 ÷ 5 = 7
As 7 is a prime number, we can stop.
Therefore, 420 is the product of all the prime numbers we found together with the final one:
⇒ 420 = 2 × 2 × 3 × 5 × 7
As 2 appears twice, we can write this using exponents:
⇒ 420 = 2² × 3 × 5 × 7