Question

Find the greatest possible length which can be used to measure exactly the lengths $7\,m,3\,m,85\,m,12\,m$ and $95\, cm$.

Answer 1

Hint: We need to find the GCF of given measurements. We find the given values in the same format of units. We find the common factors. Then we find the greatest common factor. We can also take the simultaneous factorisation of those two numbers to find the GCF.

Complete step by step answer:
We need to convert 7 m, 3 m, 85 m, 12 m 95 cm into the same unit form. We take the centimetre format. We know that 1 m is equal to 100 cm. Therefore, we get 700 cm, 300 cm, 8500 cm, 1295 cm.We also can use the simultaneous factorisation to find the greatest common factor of 700, 300, 8500, 1295. We have to divide both of them with possible primes which can divide both of them.
\[\begin{align}
  & 5\left| \!{\underline {\,
  300,700,1295,8500 \,}} \right. \\
 & 1\left| \!{\underline {\,
  60,140,259,1700 \,}} \right. \\
\end{align}\]
The only possible prime being 5.

Therefore, the greatest possible length which can be used to measure exactly the lengths 7 m, 3 m, 85 m, 12 m 95 cm is 5 cm.

Note: We need to remember that the GCF has to be only one number. It is the greatest possible divisor of all the given numbers. If the given numbers are prime numbers, then the GCD of those numbers will always be 1. Therefore, if for numbers $x$ and $y$, the GCD is $a$ then the GCD of the numbers $\dfrac{x}{a}$ and $\dfrac{y}{a}$ will be 1.