Banner 0
Banner 1
Banner 2
Banner 3
Banner 4
Banner 5
Banner 6
Banner 7
Banner 8
Banner 9
AI Mentor
Check Your IQ
Free Expert Demo
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 1288 and 575 and express it as a linear combination of them.


see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.
An Intiative by Sri Chaitanya

a

24;24 =  575 × 9 - 1288 × 4

b

23;23 =  575 × 9 - 1288 × 4

c

22;22 =  575 × 9 - 1288 × 4

d

25;25 =  575 × 9 - 1288 × 4 

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 1288 and 575 and to express it as a linear combination of 1288 and 575.
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 1288, 575    . . .  . . .(1)
1288=575×2+138   . . .  . . .(1)
∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 575 and remainder 138
575=138×4+23   . . . . . . (2)
∵  remainder ≠ 0,  apply Euclid’s division lemma on divisor 138 and remainder 23
138=23×6+0   . . . . . . (3)
∴  remainder = 0  
Hence, HCF of 1288, 575 is 23
Now, from (3)
23=575−138×4   . . . . . .(4)
Substitute (1) in (4),
23=575−(1288−575×2)×4       =575−1288×4+575×8       =575×9−1288×4  
∴  HCF of 1288 and 575 is 23 and can be expressed as a linear combination of 1288 and 575 by,
23 =  575 × 9 - 1288 × 4.
Hence the correct option is 2.
 
Watch 3-min video & get full concept clarity
score_test_img

courses

No courses found

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

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

best study material, now at your finger tips!

  • promsvg

    live classes

  • promsvg

    progress tracking

  • promsvg

    24x7 mentored guidance

  • promsvg

    study plan analysis

download the app

gplay
mentor

Download the App

gplay
whats app icon
personalised 1:1 online tutoring