Factors, Multiples, and Prime Numbers Flashcards

Question 1

What is a factor of an integer $n$?

Accepted Answer

An integer $d$ is a factor (divisor) of $n$ if $d\mid n$, meaning $n=dk$ for some integer $k$.

Question 2

State the formula for the greatest common factor (GCF) using prime factorizations.

Accepted Answer

If $a=\prod p^{\alpha_p}$ and $b=\prod p^{\beta_p}$, then
$$\gcd(a,b)=\prod p^{\min(\alpha_p,\beta_p)}$$
where $p$ runs over all primes.

Question 3

State the relationship between $\gcd(a,b)$ and $\operatorname{lcm}(a,b)$.

Accepted Answer

For positive integers $a,b$:
$$\gcd(a,b)\cdot \operatorname{lcm}(a,b)=a\cdot b.$$

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