the length breadth and height it off room are 825 675 cm and 450 cm respectively find the longest tape which can measure the three dimensions of the room exactly.
Answers
Answer:
To find the length of the longest tape which can measure the three dimensions of the room, we need to find the H.C.F of length, breadth and height of the room, i.e. 825, 675 and 450 cms respectively.
Let us factorise all three given dimensions.
825 = 3×5×5×11
675=3×3×3×5×5
450=2×3×3×5×5
Hence, 3, 5 and 5 are the common prime factors here.
So, H.C.F =3×5×5=75
Therefore, we need 75 cm longest tape to measure the three dimensions of the room.
Answer:
first we have to find the HCF of the three dimensions .
Now let us find the prime factorization of 825, 675 and 450.
825 = 3 * 5 * 5 * 11
675 = 3 * 3 * 3 * 5 * 5
450 = 2 * 3 * 3 * 5 * 5
From the above, we can say that (3×5²) is common for 825, 675 and 450. ∴HCF (825, 675, 450) = 3×5×5=75.
Hence, we got HCF = 75.
Therefore, we need 75 cm longest tape to measure the three dimensions of the room.
Hope it helps
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