Four metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?

To find the maximum number of pieces, we first need to determine the greatest possible length for each part. This length must be the Highest Common Factor (HCF) of the four rod lengths: 78, 104, 117, and 169. First, find the HCF: 78 = 13 x 6 104 = 13 x 8 117 = 13 x 9 169 = 13 x 13 The HCF of these numbers is 13. Therefore, each piece should be 13 cm long to be as long as possible. Next, calculate the number of pieces from each rod: Rod 1: 78 / 13 = 6 pieces Rod 2: 104 / 13 = 8 pieces Rod 3: 117 / 13 = 9 pieces Rod 4: 169 / 13 = 13 pieces Finally, add the number of pieces together: 6 + 8 + 9 + 13 = 36 pieces. The maximum number of pieces that can be cut is 36. Thus, option B is correct.