
Example for co-prime numbers is
A) $27,14$
B) $18,16$
C) $9,18$
D) $11,77$
Answer
444k+ views
Hint: Here we will check which one of the given options are co-prime numbers. Firstly we will write the definition of co-prime numbers then by using the factors of the numbers we will check whether they are co-prime or not. Finally we will get our desired answer.
Complete step-by-step answer:
$27,14$
We will write the factors of each number as,
$27 = 3 \times 3 \times 3 \times 1$
$14 = 2 \times 7 \times 1$
As we can see there is no common factor between the two numbers except 1.
So $27,14$ are co-prime numbers.
$18,16$
We will write the factors of each number as,
$18 = 2 \times 3 \times 3 \times 1$
$16 = 2 \times 2 \times 2 \times 2 \times 1$
As we can see there are two common factors between the two numbers which are$1,2$.
So $18,16$ are not coprime numbers.
$9,18$
We will write the factors of each number as,
$9 = 3 \times 3 \times 1$
$18 = 2 \times 3 \times 3 \times 1$
As we can see there are two common factors between the two numbers which are$1,3$.
So $9,18$ are not coprime numbers.
$11,77$
We will write the factors of each number as,
$11 = 11 \times 1$
$77 = 7 \times 11 \times 1$
As we can see there are two common factors between the two numbers which are$1,11$.
So $11,77$ are not coprime numbers.
Hence, option (A) is correct.
Note:
Co-prime numbers are those numbers whose common factor is 1 and there are no other common factors between them. We can also say that H.C.F of those numbers is 1 they are also known as ‘Relatively Prime Numbers’. Every prime number is co-prime to each other. All successive numbers are always coprime. If we add or multiply two co-prime numbers we always get a co-prime number.
Complete step-by-step answer:
$27,14$
We will write the factors of each number as,
$27 = 3 \times 3 \times 3 \times 1$
$14 = 2 \times 7 \times 1$
As we can see there is no common factor between the two numbers except 1.
So $27,14$ are co-prime numbers.
$18,16$
We will write the factors of each number as,
$18 = 2 \times 3 \times 3 \times 1$
$16 = 2 \times 2 \times 2 \times 2 \times 1$
As we can see there are two common factors between the two numbers which are$1,2$.
So $18,16$ are not coprime numbers.
$9,18$
We will write the factors of each number as,
$9 = 3 \times 3 \times 1$
$18 = 2 \times 3 \times 3 \times 1$
As we can see there are two common factors between the two numbers which are$1,3$.
So $9,18$ are not coprime numbers.
$11,77$
We will write the factors of each number as,
$11 = 11 \times 1$
$77 = 7 \times 11 \times 1$
As we can see there are two common factors between the two numbers which are$1,11$.
So $11,77$ are not coprime numbers.
Hence, option (A) is correct.
Note:
Co-prime numbers are those numbers whose common factor is 1 and there are no other common factors between them. We can also say that H.C.F of those numbers is 1 they are also known as ‘Relatively Prime Numbers’. Every prime number is co-prime to each other. All successive numbers are always coprime. If we add or multiply two co-prime numbers we always get a co-prime number.
Recently Updated Pages
You are awaiting your class 10th results Meanwhile class 7 english CBSE

Glucose when reduced with HI and red Phosphorus gives class 11 chemistry CBSE

The highest possible oxidation states of Uranium and class 11 chemistry CBSE

Find the value of x if the mode of the following data class 11 maths CBSE

Which of the following can be used in the Friedel Crafts class 11 chemistry CBSE

A sphere of mass 40 kg is attracted by a second sphere class 11 physics CBSE

Trending doubts
Full Form of IASDMIPSIFSIRSPOLICE class 7 social science CBSE

Collective noun a of sailors class 7 english CBSE

Convert 200 Million dollars in rupees class 7 maths CBSE

Fill in the blanks with appropriate modals a Drivers class 7 english CBSE

What are the controls affecting the climate of Ind class 7 social science CBSE

The southernmost point of the Indian mainland is known class 7 social studies CBSE
