Correct Answer - Option 3 : -10, 3
Given:
H.C.F of 143 and 481 is 143m + 481n
The highest common factors among the given numbers are defined as the HCF of that numbers.
Calculation:
Using factorization, HCF can be found as
143 = 11 × 13
481 = 37 × 13
HCF = 13
The given HCF 143m + 481n
So equating both HCF, we get as
143 m + 481n = 13
⇒ 13 (11m + 37n ) = 13
⇒ (11m + 37n ) = 1 ---(i)
Now substituting all values, the options that satisfies the above equation will be the final answer.
Using option 3 as (-10, 3)
m = -10
n = -3
From equation (i)
11 × (-10) + 37 × (-3) = 1, which satisfies.
So, final answer is -10, 3
