Unit 1 • Lessons 1–4 (Numbers)
Prime factors • Applications (GCF/LCM) • Rational vs. irrational • Number systems
Prime Factorization
GCF & LCM
Rationality
Real Number System
Practice + Whiteboard
Practice Set
Each question allows 2 attempts. Use the built-in whiteboard to work out your thinking, then click Reveal Solution if needed.
Symbols: ℕ (natural), W (whole), ℤ (integers), ℚ (rational), ℝ∖ℚ (irrational).
1) Prime Factors
Factorize \(360\) in exponent form.
\(360=36\cdot 10=(2^2\cdot 3^2)\cdot(2\cdot 5)=2^{\bf 3}\cdot 3^{\bf 2}\cdot 5\).
2) GCF
Find \(\mathrm{GCF}(84,\,210)\).
\(84=2^2\cdot 3\cdot 7\), \(210=2\cdot 3\cdot 5\cdot 7\Rightarrow \mathrm{GCF}=2\cdot 3\cdot 7=42.\)
3) LCM
Find \(\mathrm{LCM}(18,\,24)\).
\(18=2\cdot 3^2,\; 24=2^3\cdot 3\Rightarrow \mathrm{LCM}=2^3\cdot 3^2=72.\)
4) Rational vs. Irrational
Which number is irrational?
\(\sqrt{50}\) is not a perfect square \(\Rightarrow\) irrational. Others are rational.
5) Number Systems
Smallest set containing \(-3.5\) is…
\(-3.5=\frac{-7}{2}\) is rational. It’s not whole or integer. Smallest set: ℚ.
6) Repeating Decimals
Convert \(0.\overline{27}\) to a fraction in lowest terms.
\(0.\overline{27}=\frac{27}{99}=\frac{3}{11}\).
7) Radicals
Simplify \(\sqrt{180}\).
\(180=36\cdot 5\Rightarrow \sqrt{180}=6\sqrt{5}\).
8) Application (LCM)
Pencils in 12s; erasers in 18s. Choose the smallest combo that makes equal numbers of each.
\(\mathrm{LCM}(12,18)=36\). \(3\times12=36\) and \(2\times18=36\Rightarrow\) choice B.
Progress
Score: 0/8