Integer Properties

Question 1

When picking numbers

Answer 1

If there are multiple numbers that satisfy the constraints, pick at least 3 examples

Question 2

Identifying factors

Answer 2

1. Approximate the square root
2. Test the divisibility rules for every integer less than or equal to the square root (start with 1 and stop when you reach the square root)
3. Count the “factor buddies” as well

Question 3

Is 1 a prime number?

Answer 3

NO

Question 4

Is 2 a prime number?

Answer 4

YES

Question 5

Prime numbers under 30

Answer 5

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Question 6

To determine whether a large number is prime

Answer 6

(Use the identifying factors - approximate the square root, go from 1 to the square root and use the divisibility rules)

Question 7

Short cut for determining whether a number less than 100 is prime

Answer 7

Test 2, 3, 5, and 7

Question 8

The number of prime numbers…

Answer 8

…is infinite

Question 9

Square of any prime number…

Answer 9

…has exactly three factors

Question 10

Any division problem with a QUOTIENT of 0…

Answer 10

…can have a remainder (2/7 has a remainder of 2).

Question 11

To solve more difficult remainder problems

Answer 11

…find several integers that produce a certain remainder.
1 - generate 3 multiples of your divisor
2 - add the remainder to each

(E.g., to find integers that leave a remainder of 3 when divided by 7, pick some multiples of 7 (7, 14, 21) and add 3 to each of them (10, 17, 24)