Number theory

Question 1

Division algorithm

Answer 1

Way of expressing a large number as a multiplication in a remainder.
a=bq +r

Question 2

Euclidean algorithm used to find?

Answer 2

Greatest common divisor of two large numbers

Question 3

How to find GCD

Answer 3

We use division algorithm where the remainder becomes the factor in next line until remainder is 0, then that factor is our GCD.

Question 4

Reverse Euclidean algorithm

Answer 4

Rewrite remainder GCD line in terms of the GCD. Substitute in rearranged upper lines, solve any brackets and group like terms. Stop when GCD is expressed as multiples of two original numbers.

Question 5

How to express a base10 number in base 6

Answer 5

Do division algorithm of number, using new base as factor.
Once remainder = to number being decided we stop. We then read up division algorithm and find value of it in new base.

Question 6

Hexadecimal values past 9

Answer 6

10 = A
11 = B
12 = C
13 = D
14 = E
15 = F

Question 7

How to convert different bases back to base 10

Answer 7

Set in table of all the different powers of base, starting with 0. See how many of each level there are. Multiplying out and that will be value in base 10.

Question 8

Fundamental theory of arithmetic

Answer 8

Each number greater than 1can be expressed as a product of primes

Question 9

How to work out prime composition of an integer.

Answer 9

Divide by smallest prime possible, then divide other number left over by smallest prime. Keep doing this until only primes left over. Collect terms.