Prime Factorization

Positive Factors with PF

Step 1: prime factorize the integer

Step 2: add 1 to each exponent

Step 3: multiply those exponents together

Total factors with PF

Do positive factors with PF and multiply by 2

Three Ringing Bells

Presented with three or four numbers that occur in regular intervals. The problem usually states that all of these instances occur at the same time at some point. They then ask you how much time will elapse before they all occur simultaneously again. To solve these problems simply find the LCM of the three or four numbers.

Shared Factors with PF

Step 1: PF both numbers

Step 2: Identify what they share in common (eg 2³ and 2² both share a 2² as (2² × 2¹ ) = 2³ )

Step 3: add 1 to each exponent of the shared and then multiply the shared together

Rational vs Irrational

Rational numbers are numbers that can be written as a fraction

Irrational numbers are numbers that cannot be written as a fraction

Does it Terminate?

Step 1: Simplify the fraction to its simplest form so that there are no shared factors among the numerator and denominator

Step 2:

-only powers of 2 in deno = def terminates

-only powers of 5 in deno = def terminates

-combo of only powers of 2 and 5 in deno = def terminates

Repeating Decimal to Fraction

-Only 1 digit repeats, put it over 9

-If two digits repeat, put them over 99

-If three digits repeat, put them over 999