Chapter 5.1, Problem 1E

a.

To determine

To find: GCD of each pair of numbers

Answer to Problem 1E

GCD of given pair of numbers $=48$ .

Explanation of Solution

Given information:

  $\left(432,528\right)$

  $\left(432,528\right)$

Here $432$ can be written as

  $432=2^4\times 3^3$

  $528$ can be written as

  $528=2^4\times 3\times 11$

We got

  $432=2^4\times 3^3$

  $528=2^4\times 3\times 11$

Overlap of two expressions is $2^4\times 3$ .

Therefore,

GCD of given pair of numbers $=2^4\times 3=48$ .

b.

To determine

To find: GCD of each pair of numbers

Answer to Problem 1E

GCD of given pair of numbers $=2$ .

Explanation of Solution

Given information:

  $\left(2592,4682\right)$

  $\left(2592,4682\right)$

Here $2592$ can be written as

  $2592=2^5\times 3^4$

  $4682$ can be written as

  $4682=2\times 2341$

We got

  $2592=2^5\times 3^4$

  $4682=2\times 2341$

Overlap of two expressions is $2$ .

Therefore,

GCD of given pair of numbers $=2$ .

c.

To determine

To find: GCD of each pair of numbers

Answer to Problem 1E

GCD of given pair of numbers $=37$ .

Explanation of Solution

Given information:

  $\left(2592,4682\right)$

  $\left(999,259\right)$

Here $999$ can be written as

  $999=3^3\times 37$

  $259$ can be written as

  $259=7\times 37$

We got

  $999=3^3\times 37$

  $259=7\times 37$

Overlap of two expressions is $37$ .

Therefore,

GCD of given pair of numbers $=37$ .

d.

To determine

To find: GCD of each pair of numbers

Answer to Problem 1E

GCD of given pair of numbers $=6$ .

Explanation of Solution

Given information:

  $\left(30030,13122\right)$

  $\left(30030,13122\right)$

Here $30030$ can be written as

  $30030=2\times 3\times 5\times 7\times 11\times 13$

  $13122$ can be written as

  $13122=2\times 3^8$

We got

  $30030=2\times 3\times 5\times 7\times 11\times 13$

  $13122=2\times 3^8$

Overlap of two expressions is $2\times 3$ .

Therefore,

GCD of given pair of numbers $=2\times 3=6$ .