number propertiers

Question 1

the product of a set of n consec int is always div by n!

Answer 1

(5x6)/2!

Question 2

product of any set of consec int is div by any int in set & any combo of ints

Answer 2

n! must be div by any int or combo of int from 1 to n

Question 3

all perfect sq end in

Answer 3

0,1,4,5,6,9

Question 4

except for 0 or 1, perfect sq have [even/odd] exponents

Answer 4

even. (only way sq rt = int)

Question 5

first 8 perfect cubs

Answer 5

0/1/ 2-8/ 3-27/ 4-64/ 5-125/ 6-216/ 7-343/ 8-512

Question 6

PF of perfect cubes contain only exp that are multiples of

Answer 6

3

Question 7

decimal terminates when

Answer 7

decimal terminates iff denom of equiv. most reduced fraction has only PFs of 2,5 or both

Question 8

number patterns - remainders

Answer 8

for division, remainders will loop from 0 to n-1. if exp are involved, first figure out what pattern is eg. (3^82)/4, r=?. 3^1 / 4, r=3. 3^2 / 4, r=1. 3^3 / 4, r=3…

Question 9

units digits patterns. units digits raised to consec increasing exp follow a pattern.

Answer 9

3^1, 3. 3^2, 9. 3^3, _7. 3^4 _1. Pattern is 3,9,7,1

Question 10

remainders dividing by powers of 10

Answer 10

remainders will be last n digits of dividend, where n = 10^n

Question 11

remainders dividing by 5

Answer 11

when #s w/ same units digit div by 5, remainder is same. eg 9/5, r4. 19/5, r4.

Question 12

3 types of evenly spaced sets

Answer 12

1-consec int
2-multiples of a #
3-consec #s w/ a given remainder when div by some int (eg 1,6,11,16,21 – div by 5 r1)

Question 13

2 consec int will never share same PF

Answer 13

GCF of 2 consec int =1