Question

Express the HCF of 468 and 222 as 468x + 222y where X and Y are integers into different ways

Answer 1

Hey there !!


→ Firstly, find the HCF of 468 and 222.

▶ Using Euclid's division algorithm.


Step I : 468 = 222 × 2 + 24.

Step II : 222 = 24 × 9 + 6.

Step III : 24 = 6 × 4 + 0.


=> HCF = 6.


▶ Now, from step II, we have

=> 6 = 222 - 24 × 9.

=> 6 = 222 - [ 468 - 222 × 2 ] × 9. [ From step I ]

=> 6 = 222 - 9 × 468 + 222 × 18.

=> 6 = 222 × 19 - 9 × 468.

=> 6 = 468 × (-9) + 222 × 19.......(1).

=> HCF = 468x + 222y.........(2).

▶ From equation (1) and (2) ,

=> x = -9 and y = 19.


➡ Here, we have written

=> 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 = 213 and y = -449.


Thus, we can express the HCF in two different ways.


✔✔ Hence, it is solved ✅✅.

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$\huge \boxed{ \mathbb{THANKS}}$



$\huge \bf{ \#BeBrainly.}$

Answer 2

$\bold{ \mathbb{ACCORDING \: \: TO \: \: THE \: QUESTION:-}}$


Express the HCF of 468 and 222 as 468x + 222y where X and Y are integers into different ways



$\huge{ \mathbb{ SOLUTION;-}}$



HIGHEST COMMON FACTOR OF GIVEN NUMBER:-


468=222×2+24

222=24×9+6


Here, 24 CommOn Factor in both numbers.So it HCF


24=6*4+0



Therefore,

HCF=6


According the Question:-


6=222-(24×9)

=>222-{468-222×2)×9

=>222-{468×9-222×2×9}

=>222-(468×9)+(222×18)

=>222+(222×18)-(468×9)

=>222(1+18)=468×9

=>222×19-468×9


Arrange in particular form:-


=> -468×9+222×19

$\bold{hence}$





Here, 19 and -9 are other Integers which satisfied the x and y terms.