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Factor 62+36. Write your answer in the form a(b+c) where a is the GCF of 62 and 36.

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To factor the expression \(62 + 36\), we first need to find the greatest common factor (GCF) of the two numbers, 62 and 36.

  1. Finding the GCF:
    • The prime factorization of 62 is \(2 \times 31\).
    • The prime factorization of 36 is \(2^2 \times 3^2\).
    • The only common prime factor is \(2\).

Thus, the GCF of 62 and 36 is \(2\).

  1. Factoring the Expression: We can factor out \(2\) from the expression \(62 + 36\): \[ 62 + 36 = 2 \times (31 + 18) \]

  2. Putting it in the form \(a(b+c)\): Here, \(a = 2\), \(b = 31\), and \(c = 18\).

So, the final answer in the form \(a(b+c)\) is: \[ 2(31 + 18) \]