Number Theory

Prime Factorization and Divisors

Prime Factorization

         

72=8×9 72 = 8 \times 9

What is the largest prime factor of 72 72 ?

Which of these sets lists all of the prime factors of 120 120 ?

How many distinct prime factors does 281 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 495495?

Details and assumptions

Only add the prime factor once. For example, the sum of the prime factors of 45=32×545 = 3^2\times 5 is 3+5=83 + 5 = 8, not 3+3+5=113 + 3 + 5 = 11.

Which of these numbers has more distinct prime factors?

4556 45 \quad 56

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