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Home » So, number of 8-digit numbers **without** consecutive 3s is 55. - Abbey Badges

So, number of 8-digit numbers without consecutive 3s is 55. - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \gcd(2028, 2025) = \gcd(2025, 2028 - 2025) = \gcd(2025, 3)

📌 Now check divisibility: \( 2025 \div 3 = 675 \), remainder 0. Thus:

📌 \gcd(2025, 3) = 3

📌 Hence, the greatest common divisor is \(oxed{3}\).

📌 A community nutrition educator is organizing a cooking workshop. If the number of participants on two consecutive days are \( p \) and \( q \), and it is known that \( p + q = 150 \), what is the greatest possible value of \(\gcd(p, q)\)?

📌 Let \( d = \gcd(p, q) \). Then \( p = dk \), \( q = dl \) with \(\gcd(k, l) = 1\), and:

📌 dk + dl = 150 \implies d(k + l) = 150

📌 To maximize \( d \), minimize \( k + l \). Since \(\gcd(k, l) = 1\), the smallest sum is 2 (when \( k = 1 \), \( l = 1 \)). Then:

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