WorksheetsUnit 8: Number Theory
Total questions: 14
Worksheet time: 34mins
(8.1) Use a factor tree to find the prime factorization of 27,720. Choose all answers that apply.
2⋅2⋅2⋅3⋅3⋅5⋅7⋅11
23⋅32⋅5⋅7⋅11
2⋅3⋅5⋅7⋅11
8⋅9⋅5⋅7⋅11
(8.1) Use Prime Factorization to find
gcd(−99, 216)1
9
3
-9
-3
(8.1) All of the following numbers are prime except:
491
263
227
493
(8.1) Use the test for divisibility by 4 to determine whether or not 47,877,905,008,564,228 is divisible by 4.
Yes, the number is divisible by 4.
No, the number is not divisible by 4.
(8.2) Is 672≡12 (mod 5) ?
Yes
No
(8.2) Calculate (753 · 124 · 43,921 · 100,003) mod 10. Your answer ( r ) should be
0≤r<1036
11
6
1
(8.2) Find 194786 mod 9 .
-1
1
46,782,356,221
This is too big for my calculator and there is no other way to solve this problem easily.
(8.4) Determine the check digit of the UPC 0−14300−25433−? .
(a)
(8.4) Determine the missing digit of a money order that has ID number 829_8164036.
(a)
(8.6) Encode the message
TRUTH
using the affine cipher
C = (3P + 5) mod 26.
(a)
(8.6)
Part 1- Is C=(7P+2) mod 26 a valid affine cipher?
Yes, because gcd(7, 26)=1
No, because gcd(7, 26)=1
(8.6)
Part 2- A message was encoded using the affine cipher C=(7P+2) mod 26 . What formula can be used to decode the message?
P=(7(C−2)) mod 26
C=(15P−2) mod 26
P=(15(C−2)) mod 26
P=(15C−2) mod 26
P=(7(C+2)) mod 26
(8.6)
Part 3- Decipher the message
ZWDE
which was encoded using the affine cipher
(a)
(8.6) Decipher the message
WHV WIU LGD B
that was encoded with the
Caesar Cipher
(a)
