MATH 140 Practice Exercises for Test 2

1. Find the prime factorizations of each of the following:

a) 5100 = ________b) 627 = _________c)899 = _________

2. . Determine if 161 is a prime and briefly explain your method.

3. Find d(8700). d(8700) = _________

4. Find GCD(756,889) using the Euclidean Algorithm. ____________

5. Find LCM(51,119) by any method. ____________

6. Use the divisibility tests to determine if 1266 is divisible by 6. Explain briefly your test.

7. Perform each of the following operations in the given base .

a) 2413₅ b) 20100₁₂ c) 332₅ d) 4324₅÷32₅

3442₅ -1123₁₂ x 432₅

+1442₅

8. Explain why is undefined.

9.

10. Explain why using a pattern model.

Solutions

1. a) b) c)

2. 161 = 7x23 so it is not prime. Check for divisors up to the square root of 161.

3. so d(8700) = (2+1)(1+1)(2+1)(1+1)=36.

4. GCD(756,899)=1

5. LCM(51,119)=357.

6. 1266 is even and the sum of its digits is divisible by 3 thus it is divisible by 6.

7. a) 13402₅ b) 3422₅ c) 321024₅ d) 114₅ + Rem(21₅)

8. There is no integer c such that cx0 = -3

9. a) b) c)

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