Question

The length, breadth and height of a box are 75 cm, 85 cm and 95 cm respectively. What will be the greatest length of tape which can measure the three dimensions of the box exactly?​

Answer 1

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

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$\large{\green{\underline \bold{\tt{Given :-}}}}$

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• The length of box = 75 cm

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• The breadth of box = 85 cm

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• The height of a box = 95 cm

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$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

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• Greatest length of tape which can measure the three dimensions of the box exactly

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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〚 We need to find the Highest common factor of dimensions of box to get the greatest length of tape 〛

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Taking out prime factors of dimensions

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• 75 = 3 × 5 × 5

• 85 = 5 × 17

• 95 = 5 × 19

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Now let's have a look over HCF

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• The greatest factor common to any two or more given natural numbers is termed as HCF of given numbers.

• It is also known as Greatest Common Divisor or GCD

• To obtain the highest common factor multiply all the common prime factors with the lowest degree

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We can observe that only "5" is the Common factor in above prime factorization.

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∴ HCF = 5

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Hence is the greatest length of tape which can measure the three dimensions of the box exactly is 5 cm

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Additional information

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LCM [ Lowest common multiple ]

• The lowest common multiple will be the product of all prime factors with the highest degree

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For example let's calculate the LCM of 75 , 85 , 95

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Their prime factorization

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• 75 = 3 × 5 × 5

• 85 = 5 × 17

• 95 = 5 × 19

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In LCM we need product of all prime factors with highest degree. So, the LCM will be :

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= 3 × 5² × 17 × 19

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= 24225

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• LCM of 75 ,85 and 95 is 24225

Answer 2

$\huge{\blue{\bold{\underline{\underline{Answer :}}}}}$

$\:\:$

$\large{\green{\underline \bold{\tt{Given :-}}}}$

$\:\:$

• The length of box = 75 cm

$\:\:$

• The breadth of box = 85 cm

$\:\:$

• The height of a box = 95 cm

$\:\:$

$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

$\:\:$

• Greatest length of tape which can measure the three dimensions of the box exactly

$\:\:$

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

〚 We need to find the Highest common factor of dimensions of box to get the greatest length of tape 〛

$\:\:$

• Taking out prime factors of dimensions

$\:\:$

75 = 3 × 5 × 5

85 = 5 × 17

95 = 5 × 19

$\:\:$

Now let's have a look over HCF

$\:\:$

The greatest factor common to any two or more given natural numbers is termed as HCF of given numbers.

It is also known as Greatest Common Divisor or GCD

To obtain the highest common factor multiply all the common prime factors with the lowest degree

$\:\:$

We can observe that only "5" is the Common factor in above prime factorization.

$\:\:$

∴ HCF = 5

$\:\:$

Hence is the greatest length of tape which can measure the three dimensions of the box exactly is 5 cm

$\:\:$