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# Prime Factorization and Divisors

Learn how to break down numbers big and small, as proposed by the Fundamental Theorem of Arithmetic.

# Prime Factorization

$72 = 8 \times 9$

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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