If a number b divides into a number a evenly, then we say that a is divisible by b. There are some pretty brilliant divisibility rules that will tell us about specific numbers and their divisibility. Any ideas as to how this relates to the division algorithm and divisibility? Already registered? Course Hero is not sponsored or endorsed by any college or university. In this article, we discuss some famous facts and algorithms: Interesting Facts : All 4 digit palindromic numbers are divisible by 11. What makes the division algorithm so useful is that, as demonstrated in this proof, we can easily take a number and put it in terms of any other number. So the number of trees marked with multiples of 8 is Thendivisionof b by a is nding an integer quotient q and aremainder r satisfying the condition b =aq+r , where 0 6r 0, there is a unique q and rsuch that: 1. n = qk + r (with 0 ≤ r < k) Here n is known as dividend. Not sure what college you want to attend yet? Chapter 3 - Primes The Division Algorithm. Create your account. Further Number Theory – Exam Worksheet & Theory Guides {{courseNav.course.mDynamicIntFields.lessonCount}} lessons Let's take a look at an example pulling all this together. Because of the fundamental nature of the integers in mathematics, and the fundamental nature of mathematics in science, the famous mathematician and physicist Gauss wrote: "Mathematics is the queen of the sciences, and number theory is the queen of mathematics." A number, a, is divisible by a number, b, when b divides into a evenly. Most if not all universities worldwide offer introductory courses in number theory for math majors and in many cases as an elective course. To unlock this lesson you must be a Study.com Member. and career path that can help you find the school that's right for you. Prove that if a|b and a|c, then a|b+c and a|b-c. Pick a random number from 1 to 1000. 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