Prime Factorization - Is Number a Multiple of Both - From Variables as Factors (Level 1)

This math topic covers skills in prime factorization, identifying multiples, and using variables as factors. The problems involve determining whether a given product expressed through a combination of primes and variables is a multiple of other specified products. Each question presents expressions and asks if one is a multiple of the others, with options for yes or no answers. The focus is on understanding factorization and the principles of multiples within the context of higher-level arithmetic operations, notably within a unit focused on factoring and finding the lowest common multiples.

Is Number a Multiple of Both - From Variables as Factors

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Is z a multiple of both 14 and 4?

z=22714=274=22is z a multiple of 14 and 4?\begin{align*}z &= 2^2 \cdot 7\\\\[-0.5em]14 &= 2 \cdot 7\\[-0.5em]4 &= 2^2\end{align*}\\\\ \textsf{is }z\textsf{ a multiple of }\\14\textsf{ and }4?