Reminders

Question 1

GCF of Consecutive Integers

Answer 1

1, consecutive integers never share same prime factors (could be data sufficiency question)

Question 2

LCM

Answer 2

Each prime factor to the greatest exponent

Question 3

GCF

Answer 3

Smallest quantities of only repeated prime factors

Question 4

GCF * LCM

Answer 4

The LCM of X and Y multiplied by the GCF of X and Y is also = the product of X * Y.

24 and 30 (24*30=720)

LCM = 120
GCF = 6
(120*6=720)

Question 5

Unique prime factors

Answer 5

If given GCF and LCM only the LCM will provide all unique prime factors (could be data sufficiency question)

Question 6

What is the units digit of 3^247?

Answer 6

3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243

3-9-7-1-3-9-7-1

(Multiple of 4 is 1)

3^244 = ..1
3^245 = ..3
3^246 = ..9
3^247 = ..7

Question 7

Roots/exponents how to rationalize denominator

Answer 7

Multiply by the conjugate

/2/(2+/2) * (2-/2)/(2-/2)

… = _/2 - 1

Question 8

30-60-90 Triangle

Answer 8

Right triangle with sides: X, X _/3, 2X

Question 9

Base Fraction

Answer 9

A fraction with numerator of 1 (1/8). Every other fraction with same denominator is a multiple of the base fraction

Question 10

If 0

Answer 10

X^2

Question 11

Perfect square units digit

Answer 11

Never end in 2,3,7 or 8

Perfect squares can only have units digit of 0,1,4,5,6 or 9

Question 12

(X+Y)^2

Answer 12

X^2 + Y^2 + 2XY

Question 13

(X - Y)^2

Answer 13

X^2 + Y^2 - 2XY

Question 14

(X + Y)(X - Y)

Answer 14

X^2 - Y^2

Question 15

X-Y/Y-X

Answer 15

If X is not equal to Y:

-1

Question 16

Prime numbers 1-100

Answer 16

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Question 17

Unique prime factors of a number

Answer 17

The number of unique prime factors of a number does not change when that number is raised to a positive integer power 25 and 625 have the same unique prime factor - 5