Question

Hcf of 126 and26 in linear combination

Answer 1

Answer:

126=2×3×3×7=2×3²×7

26=2×13

HCF=product of smallest powers of each common prime factors of the numbers.

common term is 2

so HCF of 126 and 26 is 2.

Answer 2

Answer: HCF(26, 126) = 126 × 6 - 26 × 29.

Explanation:

• 126 = 26 × 4 + 22 ___(A)

As r ≠ 0, we may proceed till r = 0.

• 26 = 22 × 1 + 4 ___(B)
• 22 = 4 × 5 + 2 ___(C)
• 4 = 2 × 2 + 0. ___(D)

Therefore, HCF(126, 26) = 2.

Now, from C,

2 = 22 - 4 × 5

=> 2 = 22 - (26 - 22 × 1) × 5 [From B]

=> 2 = 22 - 26 × 5 + 22 × 5

=> 2 = - 26 × 5 + 22 × 6

=> 2 = + (126 - 26 × 4) × 6 - 26 × 5 [From A]

=> 2 = + 126 × 6 - 26 × 24 - 26 × 5

=> 2 = 126 × 6 - 26 × 29