Find the largest number which divides 615 and 963 leaving the remainder 6 in each case.

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

answer is C.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The given numbers are 615 and 963.
As per Euclid’s Division Lemma, if there are two positive integers a and b, then there exist unique q and r such that they satisfy the condition:

a = bq + r

where

0 \leq r < b

Subtract the remainder from both the given numbers. That is,

615 - 6 = 609

963 - 6 = 957

Calculation of HCF using Euclid’s division algorithm is as follows:

957 = 609 \times 1 + 348

\Rightarrow 609 = 348 \times 1 + 261

\Rightarrow 348 = 261 \times 1 + 87

\Rightarrow 261 = 87 \times 3 + 0

\Rightarrow HCF (609, 957) = 87

Therefore, 87 is the largest number which divides 615 and 963 leaving the remainder 6.
Hence, option 3 is correct.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th