# Relatively prime integers are:

(a). 6, 9

(b). 4, 9

(c). 7, 28

(d). 8, 12

Last updated date: 29th Mar 2023

•

Total views: 306.3k

•

Views today: 4.82k

Answer

Verified

306.3k+ views

Hint: Here we may use the concept that relative prime numbers are those numbers whose greatest common divisor is 1. So, here we have to check all the options whether they have a common divisor as 1 or not by using Euclid’s division algorithm.

Complete step-by-step answer:

So, let us check all the options one by one whether the numbers are relatively prime not.

So, now we may use the Euclid’s division Lemma to find the greatest common divisor of the two numbers given in each option.

Now, we should know that in Euclid’s division algorithm we apply the Euclid’s division Lemma in succession several times until we get a remainder zero. The last non-zero remainder that is obtained in this process is termed as the great common divisor of the two numbers.

So, first we should know that the according to Euclid’s division Lemma:

If we have two integers ‘a’ and ‘b’ then for these numbers there exist ‘q’ and ‘r’ such that: -

$a=bq+r$ , where q is the quotient and r is the remainder.

So, on applying this algorithm on option (a):

Using Euclid’s division Lemma we can write:

$9=6\times 1+3$

$6=3\times 2+0$

So, the last non-zero remainder obtained here is=3. So, the greatest common divisor of 9 and 6 is 3.

Hence, 9 and 6 are not relative prime numbers.

Now applying the algorithm on option (b):

Again using Euclid’s division Lemma we can write:

$9=4\times 2+1$

$4=2\times 2+0$

Here, the last non-zero remainder is 1. So, the greatest common divisor of 4 and 9 is 1.

Hence, 4 and 9 are relatively prime.

Now applying the algorithm on option (c):

Again using Euclid’s division Lemma we can write:

Here, the greatest common divisor of 28 and 7 is 7.

So, they are not relatively prime.

Now applying the algorithm on option (d):

Again using Euclid’s division Lemma we can write:

Here, the last non-zero remainder is 4. So, the greatest common divisor of 12 and 4 is 4.

Hence, they are not relatively prime.

Hence, option (b) 4, 9 is the only correct answer.

Note: Students should note here that if we get a zero remainder in the first step itself as in option (c), then the smaller of the two numbers becomes their greatest common divisor.

Complete step-by-step answer:

So, let us check all the options one by one whether the numbers are relatively prime not.

So, now we may use the Euclid’s division Lemma to find the greatest common divisor of the two numbers given in each option.

Now, we should know that in Euclid’s division algorithm we apply the Euclid’s division Lemma in succession several times until we get a remainder zero. The last non-zero remainder that is obtained in this process is termed as the great common divisor of the two numbers.

So, first we should know that the according to Euclid’s division Lemma:

If we have two integers ‘a’ and ‘b’ then for these numbers there exist ‘q’ and ‘r’ such that: -

$a=bq+r$ , where q is the quotient and r is the remainder.

So, on applying this algorithm on option (a):

Using Euclid’s division Lemma we can write:

$9=6\times 1+3$

$6=3\times 2+0$

So, the last non-zero remainder obtained here is=3. So, the greatest common divisor of 9 and 6 is 3.

Hence, 9 and 6 are not relative prime numbers.

Now applying the algorithm on option (b):

Again using Euclid’s division Lemma we can write:

$9=4\times 2+1$

$4=2\times 2+0$

Here, the last non-zero remainder is 1. So, the greatest common divisor of 4 and 9 is 1.

Hence, 4 and 9 are relatively prime.

Now applying the algorithm on option (c):

Again using Euclid’s division Lemma we can write:

Here, the greatest common divisor of 28 and 7 is 7.

So, they are not relatively prime.

Now applying the algorithm on option (d):

Again using Euclid’s division Lemma we can write:

Here, the last non-zero remainder is 4. So, the greatest common divisor of 12 and 4 is 4.

Hence, they are not relatively prime.

Hence, option (b) 4, 9 is the only correct answer.

Note: Students should note here that if we get a zero remainder in the first step itself as in option (c), then the smaller of the two numbers becomes their greatest common divisor.

Recently Updated Pages

If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?