What is the prime factorization of 350?

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.

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