sols3 - MATH 135 Solutions to Assignment 3 W10 This...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 135 Solutions to Assignment 3 W10 This assignment is due at 8:30am on Wednesday January 27, in the drop box outside the Tutorial Centre, MC 4067 Remember to show all of your computational work. The following list of the first few primes may be useful: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, . . . 1. [ 8 marks, distributed as (a) 4, (b) 2, (c) 2 ] (a) Find the prime factorization of a = 10! and b = 2 20 - 1. Hint : For b , recall that ( x 2 - y 2 ) = ( x + y )( x - y ). Answer : a = 10! = 2 8 · 3 4 · 5 2 · 7, and b = (2 5 - 1)(2 5 + 1)(2 10 + 1) = 31 · 33 · 1025 = 31 · (3 · 11)(5 2 · 41) = 3 · 5 2 · 11 · 31 · 41 (b) Find the number of positive factors of a and b . Hint : Given the prime factorization of x , x = p d 1 1 p d 2 2 p d 3 3 . . . p d n n , the number of positive factors of x is given by ( d 1 + 1)( d 2 + 1)( d 3 + 1) . . . ( d n + 1). Answer : We use the formula: thus a has (8+1)(4+1)(2+1)(1+1) = 270 factors, and b has (1 + 1)(2 + 1)(1 + 1) 3 = 48 factors (c) Find the greatest common divisor and the least common multiple of a and b . Answer
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/21/2010 for the course MATH 135 taught by Professor Andrewchilds during the Spring '08 term at Waterloo.

Page1 / 3

sols3 - MATH 135 Solutions to Assignment 3 W10 This...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online