Question

what is the greatest common factor of 32 and 44?

Explanation:

Step1: Factorize 32

Find the prime factors of 32: $32 = 2\times16 = 2\times2\times8 = 2\times2\times2\times4 = 2\times2\times2\times2\times2$, so the prime factorization of 32 is $2^5$.

Step2: Factorize 44

Find the prime factors of 44: $44 = 2\times22 = 2\times2\times11$, so the prime factorization of 44 is $2^2\times11$.

Step3: Identify common prime factors

The common prime factor between 32 and 44 is 2. The lowest power of 2 in their factorizations is $2^2 = 4$.

Answer:

4