Question

[31]. Two ribbons of prime lengths, 29 cm and 23 cm, are to be cut into the longest possible equal pieces with nothing left over. Because both lengths are prime, what is the greatest equal piece length that divides both? / अभाज्य लंबाइयों वाली दो रिबनें, 29 सेमी और 23 सेमी, बिना कुछ बचे सबसे लंबी संभव बराबर टुकड़ों में काटनी हैं। चूँकि दोनों लंबाइयाँ अभाज्य हैं, दोनों को विभाजित करने वाली सबसे बड़ी बराबर टुकड़ा-लंबाई कितनी है?

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1
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3
3.
4
4.
5
Answer (Detailed Solution Below)

Option 1 : 1

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Detailed Solution

सही उत्तर 1 है।

Key Points

The greatest common divisor of two distinct primes is 1: gcd(29, 23) = 1, since neither prime divides the other. / दो भिन्न अभाज्य संख्याओं का महत्तम समापवर्तक 1 होता है: gcd(29, 23) = 1, क्योंकि कोई भी अभाज्य दूसरे को विभाजित नहीं करता।

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Question:

[31]. Two ribbons of prime lengths, 29 cm and 23 cm, are to be cut into the longest possible equal pieces with nothing left over. Because both lengths are prime, what is the greatest equal piece length that divides both? / अभाज्य लंबाइयों वाली दो रिबनें, 29 सेमी और 23 सेमी, बिना कुछ बचे सबसे लंबी संभव बराबर टुकड़ों में काटनी हैं। चूँकि दोनों लंबाइयाँ अभाज्य हैं, दोनों को विभाजित करने वाली सबसे बड़ी बराबर टुकड़ा-लंबाई कितनी है?

1.
1
2.
3
3.
4
4.
5

Correct Answer: 1

The greatest common divisor of two distinct primes is 1: gcd(29, 23) = 1, since neither prime divides the other. / दो भिन्न अभाज्य संख्याओं का महत्तम समापवर्तक 1 होता है: gcd(29, 23) = 1, क्योंकि कोई भी अभाज्य दूसरे को विभाजित नहीं करता।

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