Number Theory
Prime Factorization and Divisors
\[ 72 = 8 \times 9 \]
What is the largest prime factor of \( 72 \)?
Which of these sets lists all of the prime factors of \( 120 \)?
How many distinct prime factors does \( 2^{8}-1 \) have?
Hint: You can use the difference of squares formula to help factor.
What is the sum of all the distinct prime factors of \(495\)?
Details and assumptions
Only add the prime factor once. For example, the sum of the prime factors of \(45 = 3^2\times 5\) is \(3 + 5 = 8\), not \(3 + 3 + 5 = 11\).
Which of these numbers has more distinct prime factors?
\[ 45 \quad 56 \]