Question

If $ 17 = 6 \times 2 + 5 $ is compared with Euclid's Division lemma $ a = bq + r $ , then which number is representing the remainder?

Answer 1

Hint: This question will be done by using Euclid's Division lemma $ a = bq + r $ , where $ q $ will be the quotient and $ r $ will be the remainder. So by comparing the equation with Euclid's Division lemma equation, we will get the value of the remainder by using it.

Complete step-by-step answer:
It states that if two integers which are positive are supposedly named as $ a $ and $ b $ , then there will be the existence of unique integers and it will be named as $ q $ and $ r $ . And it will satisfy the condition,
 $ a = bq + r $
Here, $ q $ will be the quotient and $ r $ will be the remainder
And $ a $ is the dividend and $ b $ is the divisor.
So we have the equation given as $ 17 = 6 \times 2 + 5 $ . On comparing this equation with Euclid's Division lemma $ a = bq + r $
We have the values as,
 $ \Rightarrow a = 17{\text{ , b = 6 , q = 2 and r = 5}} $
So from this, we have the remainder which will be equal to $ 5 $ .
Hence, $ 5 $ is the number which is representing the remainder.
So, the correct answer is “5”.

Note: The premise of Euclidean division calculation is Euclid's division lemma. To compute the Highest Common Factor (HCF) of two positive whole numbers $ x $ and $ y $ , Euclid's division calculation is utilized. HCF additionally called the most elevated normal factor is the biggest number which precisely partitions at least two positive numbers. By isolating both the whole numbers $ x $ and $ y $ the remainder will be zero. So these are some basics and history about Euclid's Division lemma.