Question

find x-y when HCF of 124 and 156 is 124x +156y​

Answer 1

$\Huge{\color{skyblue}{\fbox{\textsf{\textbf{♪Solution♪:-}}}}}$

Given,

• 124x +156y = H.C.F.(124,156) -----(1)

Applying Euclid's collon law on 124 and 156

we get,

$156 = 124 \times 1 + 32$

$124 = 32 \times 3+ 28$

$32 = 28 \times 1 + 4$

$28 = 4 \times 7 + 0$

→ So, H.C.F. ( 124, 156) = 4

Now,

$H.C.F.(124,156)=4 = 32 - 28 \times 1$

$\: \: \: \: \: \: = 32 - (124 - 32 \times 3) \times 1$

$\: \: \: \: \: \: = 32 - 124 + 32 \times 3$

$\: \: \: \: \: = 32 + 32 \times 3 - 124$

$\: \: \: \: \: \: = 32(1 + 3) - 124$

$\: \: \: \: \: \: = 32 \times 4 - 124$

$\: \: \: \: \: = (156 - 124 \times 1)4 - 124$

$\: \: \: \: \: = 156 \times 4 - 124 \times 4 - 124$

$\: \: \: \: \: \: = 156 \times 4 - 124(4 + 1)$

$\: \: \: \: \: \: \: = 156 \times 4 - 124 \times 5$

$\: \: \: \: \: \bold{ = 124 \times ( - 5) + 156 \times 4} \: \: \: \: - - - - (2)$

Now, comparing (1) and (2) we get ,

• x → -5
• y → 4