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Math Question: 1. What is a prime number? 2. What is a method to determine whether or not a number is a prime number? Prime Numbers Prime – A number that is only divisible by itself and 1 Composite – A number that is divisible by a number other than one and itself. Eratosthenes: A mathematician, poet, athlete, geographer, astronomer, and music theorist. He was the first person to use the word "geography" and invented the discipline of geography as we understand it. He invented a system of latitude and longitude. He was the first person to calculate the circumference of the earth by using a measuring system using stades, or the length of stadiums during that time period. He was the first to calculate the tilt of the Earth's axis. He may also have accurately calculated the distance from the earth to the sun and invented the leap day. He also created a map of the world based on the available geographical knowledge of the era. He also invented a sieve for determining prime numbers. The Sieve of Eratosthenes Prime or Composite? 77 Composite Prime or Not Prime? 97 Prime Prime or Not Prime? 147 Composite Prime or Not Prime? 197 Prime Divisibility How is a number divisible by 2? • The only Prime even number is 2 •All other even numbers are divisible by 2 •Examples: 4; 106; 1,088; 122; 10,000; 4,908,106 Divisibility How is a number divisible by 10? • Ends in a “0” in the ones place. •Examples: 10; 20; 1000; 580; 2,987,654,320 Divisibility How is a number divisible by 5? • Ends in a “0” or “5” in the ones place. •Examples: 15; 20; 1205; 565; 2,987,604,325 Divisibility How is a number divisible by 3? • Add the digits together; do they equal a multiple of 3? •Example: (285) ~ 2 + 8 + 5= 15 therefore 285 is divisible by 3 Divisibility How is a number divisible by 6? • If the Number is divisible by 2 and 3 it is also divisible by 6. •Example: 4,854 •It is even so it is divisible by 2. •Add the digits together.. 4+8+5+4=21 •21 is divisible by 3 Divisibility How is a number divisible by 9? •Add up all the digits in the number. Find out what the sum is. If the sum is divisible by 9, so is the number. •Example: 43,785 (4+3+7+8+5=27), 27 is divisible by 9, therefore 43,785 is also. Divisibility How is a number divisible by 4? •Are the last two digits in your number divisible by 4? •Example: 358,912 ends in 12 which is divisible by 4, thus so is 358,912 Divisibility How is a number divisible by 8? •If the last 3 digits are divisible by 8, so is the entire number. •Example: 6008 - The last 3 digits are divisible by 8; therefore, so is 6008. Divisibility How is a number divisible by 7? •Take the last digit in a number, Double and subtract the last digit in your number from the rest of the digits. Repeat the process for larger numbers. •Example: 357 (Double the 7 to get 14. Subtract 14 from 35 to get 21 which is divisible by 7 and we can now say that 357 is divisible by 7. Post Assessment: is the following number prime? Show your work. 757