What is the maximum length of equal pieces that can be cut from two lengths of wire of 74 cm and
92 cm with a piece of 2 cm remaining of each?
Answers
Given:
Length of two wires are 74 cm and 92 cm
A piece of 2 cm remains from each after cutting length of equal pieces
To find:
What is the maximum length of equal pieces that can be cut from two lengths of wire of 74 cm and 92 cm with a piece of 2 cm remaining of each?
Solution:
(1). After cutting length of equal pieces from each of the wires, a piece of 2 cm is remaining of each.
Therefore, the equal pieces will be cut from wires of length,
74 - 2 = 72 cm
and
92 - 2 = 90 cm
(2). Now, we will calculate the H.C.F. of 72 cm and 90 cm by using the prime factorisation method.
Factors of 72 & 90:
72 = 2 × 2 × 2 × 3 × 3
90 = 2 × 3 × 3 × 5
H.C.F.:
H.C.F. of 72 & 90 = 2 × 3 × 3 = 18
Thus, the maximum length each of the equal pieces that can be cut from two lengths of wire of 74 cm and 92 cm with a piece of 2 cm remaining of each is 18 cm.
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