Question

Find the HCF OF THE FOLLOWING PAIR'S OF INTEGERS AND EXPRESS IT AS LINEAR COMBINATION OF THEM 104 AND 1443​

Answer 1

HCF of 1443 and 104 expressed in terms of itself is 104(14) + 1443(1) = 13.

• To solve this type of questions we use Euclid's algorithm to find out the solution

1443= (104 × 13) + 91    (we express the greatest number in terms of smaller number)

104= (91 × 1) + 13  (Now we express the other number in terms of the previous remainder)

91 = (13 × 7) + 0 (Now we express the other number in terms of the previous remainder)

• Since the remainder obtained is zero , we know that the HCF of 222 and 468 is 6.

• We will use this above equations to find our solution ,

Now we take

13 = 104 - (91 × 1)

13 = 104 - {(1443 – 104 × 13) × 1 [where 1443= (104 × 13) + 91]

13 = 104 + (104 × 13) -1443

13 = 104[1 + 13] - 1443

13 = 104(14)  - 1443(1)

• Hence, HCF of 1443 and 104 in terms of itself is 104(14) + 1443(1) = 13.