Question

The product of two numbers is 2208 and their lcm is 552

Answer 1

$\mathfrak{Answer:}$

H.C.F = 4.

$\mathfrak{Step-by-Step\:Explanation:}$

$\underline{\bold{Given\;in\:the\:question:}}$

• Product of two numbers = 2208.
• Their L.C.M = 552.

$\bold{Solution:}$

Let the H.C.F be x .

$\mathfrak{According\:to\:question:}\\\\\\\boxed{\bold{H.C.F\:\times\:L.C.M=1st\;number\times2nd\:number.}}\\\\\\\implies\tt{x\times 552=2208}\\\\\\\implies\tt{x=\dfrac{2208}{552}}\\\\\\\implies\tt{x=4.}\\\\\\\\\boxed{\boxed{\bold{H.C.F=4.}}}$

$\underline{\bold{Verification:}}\\\\\\\implies\tt{H.C.F\times L.C.M=Product\:of\:no.}\\\\\\\implies\tt{4\times 552=2208}\\\\\\\therefore\quad\tt{2208=2208.}\\\\\\\bold{Hence\:verified.}\\\\\\\mathfrak{Extra\:info:}\\\\\\\tt{1.\quad L.C.M\:of\:fraction=\dfrac{L.C.M\:of\:numerators}{H.C.F\:of\;denominators}}\\\\\\\tt{2.\quad H.C.F\:of\:fraction=\dfrac{H.C.F\:of\:numerators}{L.C.M\:of\:denominators}}$

Answer 2

$\textbf{\underline{\underline{Answer :-}}}$

$\text{The HCF of given numbers is 4}$

$\textbf{\underline{\underline{Explanation :-}}}$

$\textsf{\underline{\underline{Given:}}}$

Product of the numbers = 2208

LCM of the numbers = 552

$\textsf{\underline{\underline{To find :}}}$

HCF of the number

$\textsf{\underline{\underline{Solution :}}}$

There is a relation between HCF and LCM.

The product of two given numbers is equal to the product of their HCF and LCM.

$\star$Product of two numbers = LCM × HCF

Here, the question has provided us with the product of the numbers.

Consider the HCF as y

So,

$\sf{\implies2208 = 552 \times y}$

$\sf{\implies \: y = \dfrac{2208}{552} }$

$\sf{\implies \: y = 4}$

$\large{\boxed{\bigstar{\sf\:{y = 4}}}}$

$\therefore$$\text{The HCF of given numbers is 4}$

$\textbf{\underline{\underline{Verification :-}}}$

$\sf{\implies2208 = 552 \times 4}$

$\sf{\implies2208 = 2208}$

${\boxed{\bigstar{\sf\:{LHS = RHS }}}}$

$\therefore$$\text{The HCF of given numbers is 4}$