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Question

Difficulty: EasyDivisibility, Factors, and Multiples

What is the sum of all the distinct prime factors of 3030?

  1. 10Answer
  2. B
    11
  3. C
    8
  4. D
    15
  5. E
    72

Answer

10
The prime factorization of 30 is 2 × 3 × 5. The distinct prime factors are 2, 3, and 5, and their sum is 2 + 3 + 5 = 10.

Step-by-Step Solution

1
Find the prime factorization of 30
30=2×3×530 = 2 \times 3 \times 5
Decomposing 30 into prime factors identifies all prime numbers that divide 30.
2
Identify the distinct prime factors
The distinct prime factors are 2, 3, and 5.
Prime factors are the prime numbers present in the prime factorization.
3
Calculate the sum of these distinct prime factors
2+3+5=102 + 3 + 5 = 10
The question asks for the sum of all distinct prime factors.

Key Concept

Prime Factorization and Prime Factors
Estimated Time:45s
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Topics

Divisibility, Factors, and Multiples

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