Question

Two masses of gold weighing 565 gram and 875 gram respectively are to be made into the medals of the same size. What is the weight of the largest possible medal?

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Answer 1

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Two masses of gold weighing 565 gram and 875 gram respectively are to be made into the medals of the same size. What is the weight of the largest possible medal?

$\huge\boxed{\texttt{\fcolorbox{Answer :-}}}$

Given :-

• Two masses of gold weight 565 gram and 875 gram

• Both gold are made into medals of same size

Find :-

What is the weight of the largest possible medal?

Method to be used :-

1. Find the H.C.F (Highest Common Factor ) of 565 grams and   875 grams

2. The H.C.F is the weight of the largest possible medal

Process :-

• Here is the prime factorisation of 565 :-

$\huge{\texttt{\fcolorbox{\begin{array}{r | l}5 & 565 \\\cline{2-2} 113 & 113 \\\cline{2-2} & 1\end{array}}}}$

Prime factors of 565 = 5 × 113 × 1

• Here is the prime factorisation of 875 :-

$\huge{\texttt{\fcolorbox{\begin{array}{r | l}5 & 875 \\\cline{2-2} 5 & 175 \\\cline{2-2} 5& 35\\\cline{2-2} 7& 7\\\cline{2-2} & 1\end{array}}}}$

Prime factors of 875 = 5 × 5 × 5× 7 × 1

Common factors of 565 and 875 are :-

5 × 1

⇒ Hence the H.C.F of 565 and 875 is 5

∴ The weight of largest possible medal is 5 grams

Thanks,

@RockstarPratheek

Answer 2

Answer:

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