Divisibility Rules & Prime Factorization - Pre-Algebra (6)

Misha, 6th grade ( ▀ ͜͞ʖ▀) -- ... the best way to learn is to teach --:
This video covers the divisibility rules for integers up to 12 and prime factorization, along with numerous working examples. Its best suited for elementary and middle school students.

Topics covered:
- Divisibility Rules for Integers up to 12
- Prime Factorization
- Numerous working examples

Divisibility Rules:
- Divisible by 1 - Any integer is divisible by 1
- Divisible by 2 - All even numbers are divisible by 2
- Divisible by 3 - Sum of the digits is divisible by 3
- Divisible by 4 - Last 2 digits are divisible by 4
- Divisible by 5 - Last digit is 0 or 5
- Divisible by 6 - Even number and is divisible by 3 (meaning, it passes both the 2 rule and 3 rule condition)
- Divisible by 7 - Double the last digit and subtract it from a number made by the other digits. The result must be divisible by 7.
- Divisible by 8 - Last three digits are divisible by 8.
- Divisible by 9 - Sum of the digits is divisible by 9.
- Divisible by 10 - Number ends in 0
Divisible by 11 - Add and subtract digits in an alternating pattern (add digit, subtract next digit, add next digit, etc.). Then check if that answer is divisible by 11.
- Divisible by 12 - Number is divisible by both 3 and 4 (meaning, it passes both the 3 rule and 4 rule above)

Prime Factorization is finding which prime numbers multiply together to make the original number.
Steps:
- Start with any pair of factors
- If you have a prime factor, circle it
- If you have a composite number, continue by listing a pair of factors
- Continue until each branch ends at a prime factor
- Write the prime factors using exponents smallest base to the largest base

Working Examples:
1) In the number 62A11B - replace A & B so the number is divisible by 4.
2) In the number A1B - replace A & B so the number is divisible by 7.
3) In the number 81A11B - replace A & B so the number is divisible by 9.
4) In the number 11A11B - replace A & B so the number is divisible by 11.
5) In the number 235A11B - replace A & B so the number is divisible by 3 & 5.
6) Find the prime factorization for 60.
7) Find the prime factorization for perfect square 144.
8) Find the prime factorization for 26136.
9) What is the smallest positive perfect square that is divisible by the four smallest prime numbers?
10) What positive number squared equals 96*486?