Question

hey there,
please help me out
answer this question step by step......
no spamming​

Answer 1

Qᴜᴇsᴛɪᴏɴ :-

Express HCF of 468 & 222 as 468x + 222y in two different ways where x, y are integers.

Sᴏʟᴜᴛɪᴏɴ :-

HCF of 222 and 468

➠ 468 = (222 × 2) + 24

➠ 222 = (24 × 9) + 6

➠ 24 = (6 × 4) + 0

HCF = 6

468x + 222y = 6

6 = 468x + 222y

6 = 222 - (24 × 9)

➙ 222 - {(468 - 222 × 2) × 9}

➙ 222 - (468 × 9) + (222 × 18)

➙ 222 + (222 × 18) - (468 × 9)

➙ 222 (1 + 18) - 468 × 9

➙ 222 × 19 - 468 × 9

➙ 468 × (-9) + 222 × 19

x = -9 y = 19

468x + 222y is (468 × (-9) + 222 × 19)

Answer 2

HCF of 222 + 468

468 = (222 × 2) + 24

(24 x 9) + 6

24 = (6 x 4) + 0

HCF = 6

468x + 222y = 6

6 = 468x + 222y

6=222 - (24 x 9)

→ 222-[(468 - 222 × 2) × 9}

→ 222 - (468 x 9) + (222 × 18)

→ 222 + (222 × 18) - (468 × 9)

→ 222 (1+18) - 468 × 9

→ 222 x 19 - 468 × 9

468 × (-9) + 222 × 19

x = -9

y = 19

468x + 222y is ( 468 x (-9) + 222 × 19 )