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How many distinct prime factors of 420 exist?
Correct Answer: C
Prime factorization of 420: 2, 2, 3, 5, 7
  1. A prime number is a number that is only divisible by 1 and itself. The first several prime numbers are 2, 3, 5, 7, and 11. The number 1 is not a prime number. A prime factor is a factor of a given number that is a prime number.
  2. To find the prime factors of 420, the number 420 needs to be factored. One way is to draw a factor tree. The number is factored until all the factors are prime numbers.
    Figure 1
  3. The prime factorization of 420 is:
    420 = 2*2*3*5*7
  4. The problem asks for the number of distinct prime numbers, so the number 2 is only counted once.
  5. The distinct prime numbers are 2, 3, 5, and 7, so the number of distinct prime factors is 4. Choice C.

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