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Two wires are 105 cm and 135 cm long.

Question: Two wires are 105 cm and 135 cm long. The wires need to be cut into pieces of equal length with no remainder. What is the greatest possible length of each piece?
(A) 15 cm
(B) 21 cm
(C) 27 cm
(D) 35 cm

Solution:

We need to find the HCF of 105 and 135.
Prime factorization of 105:
105=3×5×7
Prime factorization of 135:
135=3³×5
HCF is the product of the lowest powers of all common prime factors:
HCF(105,135)=3×5=15

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