Question

If thehcf of 65&117 is expressible in the form 65m-117,then find the value ofm

Answer 1

65)117(1

...-65...

52)65(1

.....-52.....

13)52(4

....-52.....

0

so H. C. F=13

13=65m-117

65m=130

m=130/65

m=2

I hope it will be answer of your question

Answer 2

$\huge\underline\mathbb {SOLUTION:-}$

Answer:

• The value of m is 2.

Given:

• The numbers 65 and 117.

Need To Find:

• The value of m = ?

Explanation:

By Euclid's division algorithm

• b = aq + r, 0 ≤ r < a

$\underline \mathsf \green {Therefore \: :-}$

[Dividend = Divisor × Quotient + Remainder]

$\implies$117 = 65 × 1 + 52

$\implies$ 65 = 52 × 1 + 13

$\implies$ 52 = 13 × 4 + 0

$\underline \mathsf \green {Therefore \: :-}$

HCF (65,117) = 13 ...(i)

Also, Given that,

HCF (65,117) = 65m - 117 ...(ii)

From Equation (i) and (ii),

65m - 117 = 13

$\implies$ 65m = 13 + 117

$\implies$ 65m = 130

$\implies$ m = $\mathsf {\cancel{\dfrac{130}{65}} }$

$\implies$ m = 2

• Hence, the value of m is 2.

Verification:

$\implies$65m - 117 = 13

$\implies$65 × 2 - 117 = 13

$\implies$130 - 117 = 13

$\implies$13 = 13

$\therefore \mathsf {L.H.S = R.H.S}$

Additional Information:

$\underline \mathsf \green {Here\: :-}$

• L.H.S is called Left Hand Side.
• R.H.S is called Right Hand Side.