# Math 110 Quiz

 Question: 1 2 3 4 5 6 Total Points: 1 1 3 1 2 2 10 Score:

1. (1 point) Use the Euclidean algorithm to find GCD(23, 17).

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2. (1 point) Suppose that x, y,m are integers, and 15x + 21y = z. What do you know

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3. (3 points) What is the exponent of 3 in the canonical decomposition of 50!?

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4. (1 point) Suppose that x and y are integers. If GCD(x, y) = 5, and LCM (x, y) = 210,
and x = 10, then what is y?

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5. (2 points) Suppose that N is a large integer. Do you think there are more primes
between 1 and N, or between N and 2N? Justify your reasoning with the prime number
theorem:

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6. (2 points) Suppose that a, b, ∈ Z, and a, b ≠ 0. Define precisely what it means to say
that  = LCM (a, b). In other words, define the “ least common multiple ”.

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