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Home » \[ a = \sqrt144 = 12 \] - Midis

\[ a = \sqrt144 = 12 \] - Midis

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Question: What is the sum of all of the positive odd divisors of $ 180 $?

📌 Solution: First, factor $ 180 = 2^2 \cdot 3^2 \cdot 5 $. To find only the odd divisors, we ignore the factor of 2 and consider only $ 3^2 \cdot 5 $.

📌 The odd divisors of 180 are the divisors of $ 3^2 \cdot 5 = 45 $.

📌 List all positive divisors of 45: $ 1, 3, 5, 9, 15, 45 $.

📌 Now compute their sum:

📌 + 3 + 5 + 9 + 15 + 45 = 78

📌 Thus, the sum of all positive odd divisors of 180 is $ \boxed{78} $.

📌 Question: What is the remainder when $ 11071 + 11073 + 11075 + 11077 $ is divided by $ 8 $?

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We use the Euclidean algorithm to find the greatest common factor (GCF...
Step 1: Divide 102 by 68:
= 68 \times 1 + 34
Remainder is 34.
Step 2: Divide 68 by 34:
= 34 \times 2 + 0
Remainder is 0.
Since the remainder is now 0, the last non-zero remainder is the GCF.
Thus, the greatest common factor of 68 and 102 is \(\boxed{34}\).**Que...
Solution:** After 4 seconds, the radius of the expanding wavefront is...

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