Four metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into…

2026

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?

  1. A.

    27

  2. B.

    36

  3. C.

    43

  4. D.

    48

Attempted by 9 students.

Show answer & explanation

Correct answer: B

Concept: To cut several rods into equal-length pieces so each piece is as long as possible, the greatest possible piece length is the Highest Common Factor (HCF) of the given rod lengths, and the maximum total number of pieces equals the sum of each rod length divided by that HCF.

Application:

  1. Factorize each rod length: 78 = 2 × 3 × 13; 104 = 23 × 13; 117 = 32 × 13; 169 = 132.

  2. Identify the factor common to all four factorizations: only 13 divides every one of 78, 104, 117 and 169, so the HCF = 13 cm — this is the greatest possible length for each piece.

  3. Divide each rod's length by the HCF to get the number of pieces cut from it: 78 ÷ 13 = 6; 104 ÷ 13 = 8; 117 ÷ 13 = 9; 169 ÷ 13 = 13.

  4. Sum the pieces from all four rods: 6 + 8 + 9 + 13 = 36.

Cross-check: Add the total length of all four rods first (78 + 104 + 117 + 169 = 468 cm) and divide by the same HCF (468 ÷ 13 = 36). This independent route gives the same total, confirming 36 is the maximum number of equal pieces.

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