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Home » Now plug in $ a = 1, b = 0 $: - Dachbleche24

Now plug in $ a = 1, b = 0 $: - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 What is the sum of all the even divisors of 60?

📌 First, find the prime factorization of 60:

📌 = 2^2 \times 3^1 \times 5^1

📌 The divisors of 60 are of the form \( 2^a \cdot 3^b \cdot 5^c \) where \( 0 \leq a \leq 2 \), \( 0 \leq b \leq 1 \), \( 0 \leq c \leq 1 \).

📌 To find the sum of even divisors, note that an even divisor must include at least one factor of 2, so \( a \geq 1 \). Thus:

📌 \( a = 1 \) or \( a = 2 \)

📌 \( b = 0 \) or \( b = 1 \)

📌 \( c = 0 \) or \( c = 1 \)

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