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If the HCF of 420 and 130 can be expressed in the form $3 x + 4,$ find $x$ .

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answer is A.

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Detailed Solution

Given,
The numbers are 420 and 130.
The HCF of the number is expressed as

3 x + 4

.
Let

a = 420

and

b = 130

,
Now as we know,
Euclid division lemma states that if we have two numbers a and b, then there exist unique integers

p

and q which satisfies the condition

a = b q + r, 0 ≤ r < b

.
Using Euclid division lemma algorithm, we get,

⇒ 420 = 130 × 3 + 30

⇒ 130 = 30 × 4 + 10

⇒ 30 = 10 × 3 + 0

⇒ H . C . F 420, 130 = 10

As the H.C.F is

3 x + 4

,
Therefore,

⇒ 3 x + 4 = 10

⇒ x = 2

The value of

x

is 2.
Therefore, option(1) is correct answer.

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