Question

three pieces of wood measuring 70m,105m,and 175 long have to be divided into pack of equal length what is the greatest possible length of each​

Answer 1

Question :- Three pieces of wood measuring 70m,105m,and 175 long have to be divided into pack of equal length what is the greatest possible length of each ?.

Solution :-

Length of the three pieces of the wood are given to be : 70m , 105m and 175m.

Now, Given that these given pieces of wood are divided into the pack of the Equal length.

We need to find the greatest possible length of each wood...

So, to find the greatest possible length of each wood we need to find the H.C.F. of the given lengths of the pieces of wood.

⇒ H.C.F. of (70 , 105 , 175)

Prime Factors of 70,105 & 175 is :-

→ 70 = 2 * 5 * 7

→ 105 = 3 * 5 * 7

→ 175 = 5 * 5 * 7

HCF = 5 * 7 = 35 .

Hence, The greatest possible length of each wood is 35m.

Answer 2

☯ GiveN :

There are three peices of woods whose measuring are 70 m, 105 m and 175 m

$\rule{200}{1}$

☯ To FinD :

We have to find the greatest possible length of each.

$\rule{200}{1}$

☯ SolutioN :

If we will find the H.C.F of the three numbers we can get the greatest possible length of each.

So, A.T.Q

→ Prime factorisation of 70

$\begin{array}{r | l} 2 & 70 \\ \cline{1-2} 5 & 35 \\ \cline{1-2} 7 & 7 \\ \cline{1-2} & 1 \end{array}$

$\rule{200}{2}$

→ Prime factorisation of 105.

$\begin{array}{r | l} 5 & 105 \\ \cline{1-2} 5 & 35 \\ \cline{1-2} 7 & 7 \\ \cline{1-2} & 1 \end{array}$

$\rule{200}{2}$

Prime factorisation of 175

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

$\rule{400}{2}$

Factors of 70 = 2 * 5 * 7

Factors of 105 = 3 * 5 * 7

Factors of 175 = 5 * 5 * 7

Now,

H.C.F = 5 * 7

H.C.F = 35

$\Large{\implies{\boxed{\boxed{\sf{35}}}}}$

$\rule{200}{2}$

★ Additional Information :

✯ Some Properties of HCF & LCM ✯

• HCF(Highest Common Factor) :- The largest or greatest factor common to any two or more given natural numbers is termed as HCF of given numbers. Also known as GCD (Greatest Common Divisor).

• LCM(Least Common Multiple) :- The least or smallest common multiple of any two or more given natural numbers are termed as LCM.

• The H.C.F. of given numbers is not greater than any of the numbers.

• The L.C.M. of given numbers is not less than any of the given numbers.

• The H.C.F. of two co-prime numbers is 1.

• LCM of fractions = ( LCM of Numerators ) / ( HCF of Denominators ) .