Banner 0
Banner 1
Banner 2
Banner 3
Banner 4
Banner 5
Banner 6
Banner 7
Banner 8
Book Online Demo
Check Your IQ
Try Test

Courses

Dropper NEET CourseDropper JEE CourseClass - 12 NEET CourseClass - 12 JEE CourseClass - 11 NEET CourseClass - 11 JEE CourseClass - 10 Foundation NEET CourseClass - 10 Foundation JEE CourseClass - 10 CBSE CourseClass - 9 Foundation NEET CourseClass - 9 Foundation JEE CourseClass -9 CBSE CourseClass - 8 CBSE CourseClass - 7 CBSE CourseClass - 6 CBSE Course
Offline Centres

Q.

Find the HCF of 592 and 252 and express it as a linear combination of them.


see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.
An Intiative by Sri Chaitanya

a

3;4 = 252 × 47 - 592 × 20

b

4;4 = 252 × 47 - 592 × 20

c

5;4 = 252 × 47 - 592 × 20

d

6;4 = 252 × 47 - 592 × 20 

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

JEE

NEET

NEET

Foundation JEE

Foundation JEE

Foundation NEET

Foundation NEET

CBSE

CBSE

Detailed Solution

Given to find the HCF of two integers 592 and 252 and to express it as linear combination of 592 and 252.
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 592, 252
592=252×2+88   . . .  . . .(1)
∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 252 and remainder 88
252=88×2+76   . . . . . . (2)
∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 88 and remainder 76
88=76×1+12   . . . . . . (3)
  ∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 76 and remainder 12
76=12×6+4   . . . . . . .(4)
  ∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 12 and remainder 4
12=4×3+0   . . . . . .(5)
∴  remainder = 0  
Hence, HCF of 592 and 252 is 12
Now, from (4), we get,
4=76−12×6   . . . . . .(6)
Substitute (3) in (6),
4=76−(88−76×1)×6 ⇒76−88×6+76×6 ⇒76×7−88×6          . . . . . .…(7)  
Substitute (2) in (7)
4=(252−88×2)×7−88×6 ⇒252×7−88×14−88×6 ⇒252×7−88×20            ……(8)  
 Substitute (1) in (8)
4=252×7−(592−252×2)×20 ⇒252×7−592×20+252×40 ⇒252×47−592×20  
∴  HCF of 592 and 252 is 4 and can be expressed as a linear combination of 592 and 252 by,
4 = 252 × 47 - 592 × 20.
Hence the correct option is 2.
 
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 Online Course for IIT JEE
Best Online Course for NEET
Best Online Course for CBSE

Ready to Test Your Skills?

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

Take Free Test

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 Online Course for IIT JEE
Best Online Course for NEET
Best Online Course for CBSE
whats app icon