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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