Consider the positive integer N = 60. Which of the following statements regarding the fact… — State PSC Exam

Consider the positive integer $N = 60$ . Which of the following statements regarding the factors and prime factorization of $N$ is/are correct?

The total number of positive factors of 60 is 12, and the prime factorization of 60 is

2^2 \times 3^1 \times 5^1

The statement declaring that the total number of positive factors is

12

is correct because

(2+1)(1+1)(1+1) = 12

. Furthermore, the statement giving prime factorization as

2^2 \times 3^1 \times 5^1

is correct as it accurately breaks down

60

into prime bases.

Find the prime factorization of

60

60 = 2^2 \times 3^1 \times 5^1

Decomposing

60

into its prime components provides the exponents needed for factor analysis.

Calculate the total number of positive factors

Total factors =

(2+1)(1+1)(1+1) = 3 \times 2 \times 2 = 12

Adding

1

to each prime exponent and multiplying gives the total count of positive factors.

Evaluate the distinct prime factors and their sum

Distinct prime factors are

2, 3, 5

, and their sum is

2 + 3 + 5 = 10

Verifying distinct prime sum shows that claiming a sum of

11

is incorrect.

Calculate the number of odd factors

Odd factors =

(1+1)(1+1) = 4

Odd factors depend only on odd prime bases (

3^1 \times 5^1

), yielding

4

odd factors (

1, 3, 5, 15

Prime Factorization and Factor Counting Formula

Question