Divisibility/Divisibility Tests

Question 1

Primality Testing

Answer 1

to test a positive integer a to see if its prime, we only need to check to see if it
is divisible by the primes p such that p^2 <= a

Question 2

n is divisible by 5 if ____

Answer 2

the rightmost digit of n is 0 or 5

Question 3

n is divisible by 2 if ____

Answer 3

the rightmost digit of n is 0, 2, 4, 6, or 8

Question 4

n is divisible by 8 if ____

Answer 4

the number formed by erasing all but the
rightmost three digits of n is divisible by 8

Question 5

n is divisible by 3 if ____

Answer 5

the sum of the digits of n is divisible by 3

Question 6

n is divisible by 4 if ____

Answer 6

the number formed by erasing all but the
rightmost two digits of n is divisible by 4

Question 7

n is divisible by 7 if ____

Answer 7

double last digit and subtract from the rest of the number. repeat until you can tell if is divisible by 7

Question 8

Prime Factorization

Answer 8

a divides b if and only if the exponents of the prime factors of a are less
than or equal to the exponents of the corresponding prime factors of b

Question 9

n is divisible by 11 if ____

Answer 9

the difference between the sum of every other
digit of n and the sum of the remaining digits is
divisible by 11

Question 10

n is divisible by 10 if ____

Answer 10

the rightmost digit is 0

Question 11

n is divisible by 9 if ____

Answer 11

the sum of the digits of n is divisible by 9

Question 12

n is divisible by 6 if ____

Answer 12

n is divisible by 2 and also by 3