What is the sum of all distinct prime factors of the integer 546? — Armed Services Vocational Aptitude Battery (ASVAB)

What is the sum of all distinct prime factors of the integer $546$ ?

Answer: 25

The integer

546

factors completely into the prime numbers

2

3

7

, and

13

. Since the question asks for the sum of all distinct prime factors, adding these together yields

2 + 3 + 7 + 13 = 25

Find the prime factorization of

546

by continuously dividing by the smallest possible prime numbers.

546 = 2 \times 273 = 2 \times 3 \times 91 = 2 \times 3 \times 7 \times 13

To identify all prime factors, we must break the number down into its foundational prime components.

Identify the distinct prime factors from the factorization.

The distinct prime factors are

2

3

7

, and

13

The question specifically asks for the sum of the 'distinct' prime factors.

Calculate the sum of these distinct prime factors.

2 + 3 + 7 + 13 = 25

Adding the identified distinct prime factors yields the final requested value.

Prime Factorization and Properties of Integers

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