Number Systems

The prime factorization of $1000$ is:

The LCM of $10$, $20$, and $30$ is:

The sum of the exponents in the prime factorization of $12$ is:

What is the prime factorization of $88$?

The prime factorization of 108 is:

The largest number that divides 245 and 1029, leaving a remainder of 5 in each case, is:

Find the HCF of 92 and 510.

If $d = HCF(a, b)$, then which of the following must be true about $d$?

If $LCM(p, q) = 221$ and $p, q$ are prime numbers with $p > q$, find $2p - 3q$.

The total number of prime factors in the expression $2^{10} \times 3^{20} \times 5^{30}$ is:

The difference $\pi - \pi$ is:

Any number that can be expressed as $p/q$ where $p, q$ are integers and $q \neq 0$ is called:

Identify the simplest form of $\sqrt{32}$.

The sum $\sqrt{49} + \sqrt{1}$ is:

If $x^2 = 5$, then the value of $x$ is:

To prove $1/\sqrt{2}$ is irrational, we can write it as $\sqrt{2}/2$. Since $\sqrt{2}$ is irrational and $2$ is a non-zero rational, their quotient is:

The statement "If $p$ is prime and $p$ divides $ab$, then $p$ divides $a$ or $p$ divides $b$" is known as:

When proving $\sqrt{3}$ is irrational, why do we conclude that $a$ must be a multiple of 3 if $a^2$ is a multiple of 3?

Which of the following describes the most common final step in the proof that $\sqrt{2}$ is irrational?

If $\sqrt{a}$ and $\sqrt{b}$ are irrational, what can be said about $\sqrt{a} + \sqrt{b}$ in a general algebraic proof?

The decimal representation of $\frac{3}{2^2 \times 5^1}$ is:

What is the decimal expansion of $\frac{11}{5}$?

Which of the following fractions will have a terminating decimal?

The fraction $\frac{27}{60}$ is equivalent to which decimal?

If $x = 3^{1/3} + 3^{-1/3}$, find the value of the expression $3x^3 - 9x$.

Simplify $\sqrt{10} \times \sqrt{15}$ and express in simplest surd form.

Find the value of $(1/64)^{-1/3}$.

The units digit of the number $3^{101}$ is:

If $n$ is the smallest natural number such that $n \times 27$ is a perfect cube, what is the value of $n$?

Find the sum of the exponents of prime factors in the prime factorization of 196.