Math, asked by frostbeast55, 1 year ago

Use Euclids algorithm to find HCF of 1190 and1445.Express the HCF in form of 1190m+1445n.

Answers

Answered by sivaprasath
6
Solution :

_____________________________________________________________

Given :

To use euclid's division algorithm to find HCF of 1190 & 1445 & To express them in the form m & n,.

_____________________________________________________________

We , know that,

⇒ a = bq + r

where,. a > b > r ≥ 0

So,

∴ a = 1445

∴ b = 1190

Using euclid algorithm we get,

⇒ 1445 = 1190 x 1 + 255

⇒ 1190 = 255 x 4 + 170

⇒ 255 = 170 x 1  + 85

⇒ 170 = 85 x 2 + 0

∴ HCF{1445,1190} = 85

Hence,.

By in linear form,.

⇒ 85 = 1190 x (-6) + 1445 x (5)

∴ m = -6 & ∴ n = 5

_____________________________________________________________

                                 Hope it Helps !!

⇒ Mark as Brainliest,.

frostbeast55: yes it helped but how can I mark it brainlist
sivaprasath: just wait for other answer to complete
sivaprasath: then,
sivaprasath: you will see a button, as MARK AS BRAINLIEST(with a crown symbol, above my answer)
sivaprasath: just click on it,.
frostbeast55: ok
sivaprasath: thanks,.
Answered by mindfulmaisel
4

Given:

Two numbers

a = 1190

b = 1445

To find:        

Highest common factor (HCF) of a and b.

Express it in form of 1190m +1445n.

Solution:

1445=(1190 \times 1)+255

1190=(255 \times 4)+170

255=(170 \times 1)+85

170=(85 \times 2)+0

HCF = 85

Now,                                    

85 = 255 - 170

= (1445-1190)-(1190-255 \times 4)

=1445-1190-1190+255 \times 4

=1445-1190 \times 2+(1445-1190) \times 4

=1445-1190 \times 2+1445 \times 4-1190 \times 4

=1445 \times 5-1190 \times 6

=1190 \times -6+1445 \times 5

=1190m + 1445n

m = -6 \quad and \quad n = 5

Similar questions