Book Online Demo
Check Your IQ

Courses

Class - 11 JEE CourseClass - 11 NEET CourseClass - 12 JEE CourseClass - 12 NEET CourseDropper JEE CourseDropper NEET CourseClass - 10 Foundation JEE CourseClass - 10 Foundation NEET CourseClass - 10 CBSE CourseClass - 9 Foundation JEE CourseClass -9 CBSE CourseClass - 8 CBSE CourseClass - 7 CBSE CourseClass - 6 CBSE Course

Q.

Find the HCF of 963 and 657 and express it as a linear combination of them.


see full answer

Want to Fund your own JEE / NEET / Foundation preparation ??

Take the SCORE scholarship exam from home and compete for scholarships worth ₹1 crore!*
An Intiative by Sri Chaitanya

a

9;9 = 657 × 22 – 963 × 15

b

8;8 = 657 × 22 – 963 × 15

c

7;7 = 657 × 22 – 963 × 15

d

6;6 = 657 × 22 – 963 × 15 

answer is A.

(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

Given to find the HCF of two integers 963 and 657 and to express it as linear combination of 963 and 657.
Euclid's Division Lemma states that if two positive integers a and b exist, then there must be unique values of q and r that satisfy the formula a= bq + r, where  0 ≤ r < b.
Apply Euclid’s division lemma on 963, 657
963=657×1+306   . . .  . . .(1)
∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 657 and remainder 306
657=306×2+45   . . . . . . (2)
∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 306 and remainder 45
306=45×6+36   . . . . . . (3)
∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 45 and remainder 36
45=36×1+9   . . . . . . .(4)
∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 36 and remainder 9
36=9×4+0   . . . . . .(5)
∴  remainder = 0  
∴  HCF of 963, 657 is 9
Now, equation (4) can be expressed as,
9=45−36×1   . . . . . .(6)
Substitute (3) in (6)
9=45−(306−45×6)×1     ⇒45−306×1+45×6   . . . . . . (7)
 Substitute (2) in (7)
9=(657−306×2)×7−306×1  
⇒657×7−306×14−306×1   ⇒657×7−306×15……(8)  
 Substitute (1) in (8)
  9=657×7−(963−657×1)×15 ⇒657×7−963×15+657×15 ⇒657×22−963×15  
∴  HCF of 963 and 657 is 9 and can be expressed as a linear combination of 963 and 657 by,
9 = 657 × 22 – 963 × 15.
Hence the correct option is 1.
 
Watch 3-min video & get full concept clarity
Related Blogs
Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation
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
score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

Related Blogs
Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation
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
whats app icon