Chapter II, Problem 1E

a.

To determine

To write the number as a product of primes and list eight divisors (if composite).

Answer to Problem 1E

  $672=2\times 2\times 2\times 2\times 2\times 3\times 7$

Eight divisors of 672 are $\left\{2,3,4,6,7,8,14,21\right\}$ .

Explanation of Solution

Given :

The number is 672 .

672 can be written as a product of primes as follows :

  $672=2\times 2\times 2\times 2\times 2\times 3\times 7$

Also, the given number is composite.

Hence, the set of any eight divisors of 672 is $\left\{2,3,4,6,7,8,14,21\right\}$ .

b.

To determine

To write the number as a product of primes and list eight divisors (if composite).

Answer to Problem 1E

  $673=1\times 673$ is a prime number.

Explanation of Solution

Given :

The number is 673 .

Since, 673 is a prime number.

Therefore, it can be written as follows :

  $673=1\times 673$

c.

To determine

To write the number as a product of primes and list eight divisors (if composite).

Answer to Problem 1E

  $675=3\times 3\times 3\times 5\times 5$

Eight divisors of 675 are $\left\{3,9,15,25,27,45,75,135\right\}$ .

Explanation of Solution

Given :

The number is 675 .

675 can be written as product of primes as follows :

  $675=3\times 3\times 3\times 5\times 5$

Also, the given number is composite.

Hence, the set of any eight divisors of 675 is $\left\{3,9,15,25,27,45,75,135\right\}$ .