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?

\[ 45 \quad 56 \]

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