Chapter 4, Problem 4CST

To determine

To determine which numbers are relatively prime

Answer to Problem 4CST

F. 25,36

Explanation of Solution

Given Information: Four parts

F. 25,36

G. 12,20

H. 24,28

I. 45,84

Formula Used: Greatest Common Divisor

Calculation:

Two numbers are said to be relatively prime if their Greatest Common Divisor is 1. To identify, which of the following options are relative prime, find their GCF one by one.

F. 25, 36

Let us first write down the prime factors of each, to identify their GCF.

  $25=5\times 5$

36 may be written as

  $36=2\times 2\times 3\times 3$

As visible, there are no common factors between 25 & 36, so their GCF is 1. Hence , 25 & 36 are relatively prime.

F. 25, 36

Let us first write down the prime factors of each, to identify their GCF.

  $25=5\times 5$

36 may be written as

  $36=2\times 2\times 3\times 3$

As visible, there are no common factors between 25 & 36, so their GCF is 1. Hence , 25 & 36 are relatively prime.

G.12,20

Let us first write down the prime factors of each, to identify their GCF.

  $12=2\times 3\times 2$

20 may be written as

  $20=5\times 2\times 2$

As visible, $2\times 2$ is common factors between 12 & 20, so their GCF is 4. Hence ,12 & 20 are not relatively prime.

H. 24,28

Let us first write down the prime factors of each, to identify their GCF.

  $24=2\times 3\times 2\times 2$

28 may be written as

  $28=7\times 2\times 2$

As visible, $2\times 2$ is common factors between 24 & 28, so their GCF is 4. Hence ,24 & 28 are not relatively prime.

I. 45,84

Let us first write down the prime factors of each, to identify their GCF.

  $45=5\times 3\times 3$

84 may be written as

  $84=7\times 2\times 2\times 3$

As visible, 3 is common factors between 45 & 84, so their GCF is 3. Hence ,45 & 84 are not relatively prime.