The prime factorization of 500 can be found by continuously dividing the number by its smallest prime factors until we’re left with 1.
First, we can start by dividing 500 by 2, the smallest prime number:
- 500 ÷ 2 = 250
Next, we continue with 250:
- 250 ÷ 2 = 125
Since 125 is no longer divisible by 2 (as it’s an odd number), we move on to the next prime number, which is 3. However, 125 is not divisible by 3, so we try 5:
- 125 ÷ 5 = 25
We then take 25 and divide it by 5 again:
- 25 ÷ 5 = 5
Finally, we divide 5 by 5:
- 5 ÷ 5 = 1
Putting it all together, we have:
- 500 = 2 × 2 × 5 × 5 × 5
In prime factor notation, this is often written as:
- 500 = 22 × 53
So the prime factorization of 500 is 22 × 53.