What is the sum of all distinct prime factors of 420? — GRE General Test

What is the sum of all distinct prime factors of $420$ ?

The sum of all distinct prime factors of

420

17

The prime factorization of

420

2^2 \times 3 \times 5 \times 7

. The distinct prime numbers in this factorization are

2

3

5

, and

7

. Adding these values together yields

2 + 3 + 5 + 7 = 17

Find the prime factorization of

420

420 = 2^2 \times 3 \times 5 \times 7

Decompose

420

into prime components:

420 = 10 \times 42 = (2 \times 5) \times (2 \times 3 \times 7) = 2^2 \times 3 \times 5 \times 7

Identify the set of distinct prime factors.

The distinct prime factors are

2, 3, 5,

and

7

Exponents are ignored when selecting unique prime factors.

Calculate the sum of the distinct prime factors.

2 + 3 + 5 + 7 = 17

Add the unique prime factors together.

Prime Factorization

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