Three ribbons 171cm,185cm & 199cm long are to be cut into equal pieces of maximum possible length ,leaving bits of ribbons 3 cm long from each.What would be the length of each piece of ribbon& how many such pieces can one get?
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Answer:
14 cm x 39 pieces
Step-by-step explanation:
3 cm cut from each ribbon:
- 171 cm- 3 cm= 168 cm
- 185 cm- 3 cm= 182 cm
- 199 cm- 3 cm= 196 cm
Prime factors of each number:
- 168 = 2 × 2 × 2 × 3 × 7
- 182 = 2 × 7 × 13
- 196 = 2 × 2 × 7 × 7
HCF(168, 182, 196)= 2 × 7 = 14 cm maximum possible length of each piece
- 168 cm = 14 cm × 12
- 182 cm = 14 cm × 13
- 196 cm = 14 cm × 14
Total pieces= 12+13+14= 39
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