Euclid's Lemma and Number Theory Quiz

• $p$ divides $a$ and $b$
• both $a$ and $b$ are prime numbers
• $p$ does not divide $a$ and $p$ does not divide $b$
• $p$ divides $a$ or $p$ divides $b$ (correct)

• Every integer greater than 1 is a prime or a product of primes, and this product is not unique.
• Every integer greater than 1 is a prime or a product of primes, and this product is unique. (correct)
• Every integer is a prime number.
• Every integer is a composite number.

• $6$ divides $4$ and $3$
• $6$ is not a prime number
• $6$ does not divide $(4 \times 3)$
• $6$ divides $(4 \times 3)$ but does not divide $4$ or $3$ (correct)

<p>It may not hold true (A)</p> Signup and view all the answers

<p>Primes are the building blocks for all integers (C)</p> Signup and view all the answers