To find the prime factorization of 350, we start by dividing the number by the smallest prime number, which is 2. Since 350 is even, we can divide it by 2:
- 350 ÷ 2 = 175
Now, we have 175. We need to factor this number next. We check for prime factors starting with the smallest primes:
- 175 is not divisible by 2 (it’s odd).
- Next, we try 3. Adding the digits of 175 gives us 1 + 7 + 5 = 13, which is not divisible by 3.
- Now we try 5. Since 175 ends with a 5, we can divide it:
- 175 ÷ 5 = 35
Next, we factor 35:
- 35 ÷ 5 = 7
At this point, we have reached 7, which is a prime number. Therefore, the complete prime factorization of 350 is:
- 350 = 2 × 5 × 5 × 7
We can also express this in exponential form as:
- 350 = 2 × 5² × 7
So the prime factors of 350 are 2, 5 (twice), and 7.