quant flashcard notes: group 2

Divisibility Rules

• 0 —> nothing is divisible by 0

• 1: all integers

• 2: all even integers

• 3: sum of digits divisible by 3

• 4: last two digits divisble by 4

• 5: last digit 0 or 5

• 6: divisible by both 2 and 3

• 7: not divisible by 2 or 3 (easier to do via calculator)

• 8: last three digits divisible by 8 (easier to do via calculator)

• 9: sum of digits divisible by 9

• 10: last digit 0

Prime Numbers (1-100)

2,3,5,7,11,13,17,19,23,27,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97

• 2 is the only even prime number!!!

• composite number = non-prime

• When you multiply prime #’s together and add 1, you create a new prime #

  • (2)(3)(5) + 1 = 31

How many n in a Factorial?

• How many 3s are there in 30!

  • 3^1 = 10 —> 3 goes into 30 10 times

  • 3² (9) = 3 —> 9 goes into 30 3 times (9×3=27)

  • 3³ (27) = 1 —> 27 goes into 30 1 time

    • 10 + 3 +1 = 14 total

Zero is Weird!

• neither + or -

• even

• multiple of every integer

• factor of zero

• cannot be divided into anything

• zero as an exponent equals one

• 0! = 1

GCF with PF

What’s the GCF of 720 and 1764?

• Step 1: Prime factorization

  • 2^4 3² 5^1 (720)

  • 2² 3² 7² (1764)

• Step 2: Take what they have in common

  • 2²3² = 36

LCM with PF

What’s the LCM of 126 and 132?

• Step 1: Prime factorization

  • 2^1 3² 7^1 (126)

  • 2² 3^1 11^1 (132)

• Step 2: Take greatest number of each prime

  • 2² 3² 7^1 11^1 = 2,772

Exponents and Unit Digits

No matter how large the numbers get, you can easily find the unit digit by any arithmetic operations by just focusing on the last digits

• 0^n = always 0

• 1^n = always 1

• 2² = 2,4,6,8

• 3^n = 3,9,7,1

• 4^n = 4,6,4,6

• 5^n = always 5

• 6^n = always 6

• 7^n = 7,9,3,1

• 8^n = 8,4,2,6

• 9^n = 9,1,9,1