CBSE Class 10 Answered
find the h.c.f of 468 and 222 and express it in the form 468*213-222*449
Asked by vardhansachin2005 | 05 Jun, 2019, 10:25: AM
Expert Answer
Using Euclid's division algorithm.
(1) 468 = 222 × 2 + 24.
(2) 222 = 24 × 9 + 6.
(3) 24 = 6 × 4 + 0.
HCF = 6.
from step 2, we have
6 = 222 - 24 × 9.
6 = 222 - [ 468 - 222 × 2 ] × 9. [ From step 1]
6 = 222 - 9 × 468 + 222 × 18.
6 = 222 × 19 - 9 × 468.
6 = 468 × (-9) + 222 × 19.......(a)
HCF = 468x + 222y.........(b)
(2) 222 = 24 × 9 + 6.
(3) 24 = 6 × 4 + 0.
HCF = 6.
from step 2, we have
6 = 222 - 24 × 9.
6 = 222 - [ 468 - 222 × 2 ] × 9. [ From step 1]
6 = 222 - 9 × 468 + 222 × 18.
6 = 222 × 19 - 9 × 468.
6 = 468 × (-9) + 222 × 19.......(a)
HCF = 468x + 222y.........(b)
From equation (a) and (b)
x = -9 and y = 19
now,
6 = xa + yb.
6 = xa + yb + ab - ab.
6 = xa + ab + yb - ab.
6 = a( x + b ) + b( y - a ).
6 = 468( -9 + 222 ) + 222( 19 - 468 )
6 = 468 × 213 + (-449) × 222
x = -9 and y = 19
now,
6 = xa + yb.
6 = xa + yb + ab - ab.
6 = xa + ab + yb - ab.
6 = a( x + b ) + b( y - a ).
6 = 468( -9 + 222 ) + 222( 19 - 468 )
6 = 468 × 213 + (-449) × 222
Answered by Arun | 06 Jun, 2019, 09:18: AM
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