# Week 2 Worksheet

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Week 2 MATH 1051 Worksheet 1. Determine how many divisors each number has, and then whether each number is perfect, deficient, or abundant: (a) 128 (b) 675 (c) 196 (d) 385 (e) 496 (f) 510 (g) 2783 2. Use the Primes Factors method to find the gcd and lcm of the following numbers. (a) 360, 1134 (b) 308, 1089, 2200 3. Use the Dividing by Primes method to find the gcd and lcm of the following numbers. (a) 495, 720, 990 (b) 1573, 2145, 2860 4. Use the Euclidean Algorithm to find the gcds of the following numbers. Then use the result to find their lcms. (a) 6877 and 95381 (b) 78973 and 55961 5. Use any mnethod to find the greatest common divisor and least common multiple of each set of numbers: (a) 400 and 110 (b) 136 and 544 (c) 6845 and 16169 (d) 450, 630 and 1155 Apply your knowledge 6. Two numbers x and y are amicable if the sum of the proper divisors of x is y and the sum of the proper divisors of y is x . Show that 284 and 220 are amicable. 7. Find a number greater than 100 that is relatively prime to 41745. 8. If p , q , r , and s are prime, find the least common multiple of the numbers: p 3 q 7 s 5 , p 5 qr 2 s 3 , and q 2 r 3 s 4 . 9. If x and y are relatively prime, then find their gcd and lcm. 1