Answer
Verified
333.2k+ views
Hint: As we know that the HCF is the highest common factor i.e the highest common number which divides two or more numbers. Here we will use Euclid’s division lemma to the above question and we will get the answer.
Complete step-by-step answer:
Let us consider the above question we have
d = HCF of 24 and 36
we have to find a and b such that $d=24a+36b$
Now we will apply the Euclid’s division lemma to 24 and 36, we get
\[\begin{align}
& 36=24(1)+12....................(1) \\
& 24=2(12)+0 \\
\end{align}\]
Thus the HCF of 24 and 36 is 12.
From the equation (1) we have,
\[\begin{align}
& \Rightarrow 12=36-24 \\
& \Rightarrow 12=24(-1)+36(1) \\
& \Rightarrow 12=24a+36b \\
\end{align}\]
Where a= -1 and b= 1.
Therefore the two numbers a and b are -1 and 1 respectively.
Note: Be careful while doing calculation as there is a chance that you might make mistakes during the calculation and you will get the incorrect answer. Just remember the concept of Euclid’s division lemma as it is very helpful in these types of questions. Also remember the concept of HCF ( highest common factor) and the way to find it. Also remember the fact that a natural number, greater than 1, can always be written as the sum of greatest common divisor and lowest common multiple of two natural numbers.
Complete step-by-step answer:
Let us consider the above question we have
d = HCF of 24 and 36
we have to find a and b such that $d=24a+36b$
Now we will apply the Euclid’s division lemma to 24 and 36, we get
\[\begin{align}
& 36=24(1)+12....................(1) \\
& 24=2(12)+0 \\
\end{align}\]
Thus the HCF of 24 and 36 is 12.
From the equation (1) we have,
\[\begin{align}
& \Rightarrow 12=36-24 \\
& \Rightarrow 12=24(-1)+36(1) \\
& \Rightarrow 12=24a+36b \\
\end{align}\]
Where a= -1 and b= 1.
Therefore the two numbers a and b are -1 and 1 respectively.
Note: Be careful while doing calculation as there is a chance that you might make mistakes during the calculation and you will get the incorrect answer. Just remember the concept of Euclid’s division lemma as it is very helpful in these types of questions. Also remember the concept of HCF ( highest common factor) and the way to find it. Also remember the fact that a natural number, greater than 1, can always be written as the sum of greatest common divisor and lowest common multiple of two natural numbers.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Assertion CNG is a better fuel than petrol Reason It class 11 chemistry CBSE
How does pressure exerted by solid and a fluid differ class 8 physics CBSE
Number of valence electrons in Chlorine ion are a 16 class 11 chemistry CBSE
What are agricultural practices? Define
What does CNG stand for and why is it considered to class 10 chemistry CBSE
The rate of evaporation depends on a Surface area b class 9 chemistry CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
State whether the following statement is true or false class 11 physics CBSE
A night bird owl can see very well in the night but class 12 physics CBSE