Question

The length, breadth and height of a room are 976 cm, 793 cm and 183 cm respectively. Find the longest tape which can measure the three dimensions of the room exactly.

Answer 1

Answer:

The length, breadth and height of a room are 976 cm, 793 cm and 183 cm respectively. The longest tape which can measure the three dimensions of the room exactly is 61 cm.

Step-by-step explanation:

To find the longest tape that can measure 976, 793 and 183 exactly without a remainder, we have to find the Highetst Common Factor ( Greatest Common Divisor/Measure) of these three numbers

To find the Greatest Common Divisor/Highest Common Factor, we will need to calculate the factors of each of these numbers:

The factors of 976 are 1, 2, 4, 8, 16, 61, 122, 244, 488, 976.

The factors of 793 are 1, 13  61, 793.

The factors of 183 are 1, 3, 61, 183.

The Higest common factor of these three numbers is 61

Therefore a tape measure that is 61 cm long is able to measure these three dimensions exactly.

Answer 2

$➪ \sf \red{Answer:-}$

$\huge{ ➫} \tt GIVEN:-$

$length \: of \: room \: = 7m25cm = 725cm \\ breadth \: of \: room \: = 9m25cm = 925cm \\ height \: of \: room \: = 8m25cm = 825cm$

$\huge ➫ \sf FIND:-$

$now \: we \: find \: HCF \: of \: 725,925 \: and \: 825$

${\huge ➫ {\mathfrak{Solution:-}}}$

$725 = 5 \times 5 \times29$

$925 = 5 \times 5 \times 37$

$825 = 3 \times 5 \times 5 \times 11$

$so, \: heighest \: common \: factor \: is \: 5 \times 5 = 25$

$therefore \: HCF \: of \: 725,925,825 \: is \: 25.$

$\therefore 25m is \: the \: longest \: tape \: measure \: which \: can \: measure \: all \: the \: dimensions.$

$so, \: answer \: is \: \boxed{ \mathfrak{ 25m}}$