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No Cost to Join: Try These Free Color Games That Will Keep You Entertained! - Treasure Valley Movers

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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📌 Let \( k = 10a + b \), where \( a \in \{1,2,\dots,9\} \), \( b \in \{0,1,\dots,9\} \), so sum of digits is \( a + b \).

📌 We check two-digit numbers \( k \equiv 2 \pmod{7} \): they are:

📌 k = 16, 23, 30, 37, 44, 51, 58, 65, 72, 79, 86, 93

📌 Now test each for divisibility by digit sum:

📌 \( k = 16 \): digit sum = \( 1+6 = 7 \), \( 16 \div 7 \approx 2.28 \), not divisible.

📌 \( k = 23 \): sum = \( 2+3 = 5 \), \( 23 \div 5 = 4.6 \), no.

📌 \( k = 30 \): sum = \( 3+0 = 3 \), \( 30 \div 3 = 10 \), yes!

📌 So \( k = 30 \) is divisible by digit sum (3), and \( 30 \div 7 = 4 \times 7 + 2 \Rightarrow 30 \equiv 2 \pmod{7} \).

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