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

This math topic practices the skill of determining whether one number is a factor of other numbers, using prime factorization. Each problem presents prime factorizations of multiple numbers and asks if a specific factor is common to two given numbers. The learner must understand how to break numbers into their prime factors and check commonality between factorized forms.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

Is Number a Factor of Both - From Variables as Factors

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Is r a factor of both 105 and 165?

r=2⋅3105=3⋅5⋅7165=3⋅5⋅11is r a factor of105 and 165?\begin{align*}r &= 2 \cdot 3\\[-0.5em]105 &= 3 \cdot 5 \cdot 7\\[-0.5em]165 &= 3 \cdot 5 \cdot 11\end{align*}\\\\ \textsf{is }r\textsf{ a factor of}\\105\textsf{ and }165?