If an integer n is expressed in its prime factorization as n = 2^3 \times 5^2 \times 11, h… — GMAT

If an integer $n$ is expressed in its prime factorization as $n = 2^3 \times 5^2 \times 11$ , how many distinct prime factors does $n$ have?

A
2
3Answer
C
4
D
6
E
30

Answer

The integer has 3 distinct prime factors.

The expression

n = 2^3 \times 5^2 \times 11

shows

n

written as a product of prime powers. The distinct prime factors are the unique prime numbers serving as bases in this expansion: 2, 5, and 11. Therefore, there are exactly 3 distinct prime factors.

Step-by-Step Solution

Identify the prime bases in the prime factorization of

n

The prime factorization is given as

n = 2^3 \times 5^2 \times 11^1

. The prime bases are

2

5

, and

11

By definition, the prime factorization expresses a number as a product of prime numbers raised to exponents.

Count the number of unique prime bases.

There are 3 unique prime numbers (

2

5

, and

11

Exponents indicate how many times a prime factor is multiplied, but they do not add new distinct prime factors.

Key Concept

Distinct Prime Factors

Estimated Time:45s

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