Question

The H.C.F of the two number is 17 and their product is 4624.what is the sum of reciprocals?

Answer 1

Answer:

Lcm = product of the number/ their hcf

= 4624/17

= 272

now,

17a * 17b = 4624

ab = 16

a = 1, b = 16

so, the numbers will be = 17 & 272

Now find their sum of reciprocal as your homework...

( mark as brainlist )

Answer 2

Answer:$\dfrac{1}{16}$

Step-by-step explanation:

Given that 17 is the HCF of two numbers

Therefore the numbers will be 17 x and 17 y where x any y are co prime

Now the product of two numbers is 4624

As we know

LCM X HCF = Product of two numbers

$LCM \times 17 = 4624 \\\\\Rightarrow LCM = 272$

Now $17x \times 17y = 4624 \\\\\Rightarrow xy = 16$

possible values of x and y (1,16), (2,8),(4,4)

But x and y are coprime therefore we take x= 1 y = 16

first number is 17x = 17 x 1 = 17

second number is 17y = 17 x 16 = 272

Now sum of reciprocals

$\dfrac{1}{17} +\dfrac{1}{272} =\dfrac{16+1}{272} = \dfrac{17}{272} = \dfrac{1}{16}$

Hence, the sum of reciprocals is $\dfrac{1}{16}$