Wednesday, 9 January 2013

PRIME, HCF, LCM - SIEVE

INTRODUCTION
Search the definition of the following using reliable websites (post as comments and remember to quote the sites in your comments)
1. PRIME NUMBER
2. COMPOSITE NUMBER

Question:
3. Are all odd numbers prime? Justify
4. Are all even numbers composite numbers? Justify

SIEVE OF ERASTOTHENES
View the following video before completing the exercise in the booklet.
Exercise Respect and Responsibility while watching

18 comments:

1. 1&2:
A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime because only 1 and 5 divide it, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6.
http://en.wikipedia.org/wiki/Prime_number
3:Since a prime number is a number that that can be divided by 1or itself, then the rule does not apply to some of the odd numbers:9, 15, 21, and 27
4:No,not all even numbers are composite numbers. one example is the number two. It may be an even number, but it is a prime number, as it is only able to be divided by the number 1 and itself,2.

2. Definition of a prime number : A prime number is a number is a number whose only factors are 1 and itself. That means there is no whole number that evenly divides the prime number. (source:http://www.mathwarehouse.com/arithmetic/numbers/prime-number/)
Definition of a composite number : A Composite Number can be divided evenly by numbers other than 1 or itself.
Example: 9 can be divided evenly by 1, 3 and 9, so 9 is a composite number.
But 7 can only be divided evenly by 1 and 7, so 7 is NOT a composite number (it is a Prime Number).
(source:http://www.mathsisfun.com/definitions/composite-number.html)
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Are all odd numbers prime ? : Its a yes and now i guess . Considering that all even numbers are divisible by 2 , it means that the only even prime number is 2 itself as a prime number must only have two factors - one and itself . All the other prime numbers are odd numbers . So , yes and no to the question but mainly yes , all prime numbers are odd except for one (two)

Are all even numbers composite numbers ? : Again , yes and no . Most even numbers are composite numbers except for numbers like 27 and 49 which are composite numbers but are odd numbers , not even numbers . In addition , 2 is an even number but it is not a composite number - it is a prime number .

3. A prime number is a natural number greater than 1 that has no other divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number.
http://en.wikipedia.org/wiki/Prime_number

Not all odd numbers are prime numbers, eg. 9, 15, 21 can be divided by more than one number. http://wiki.answers.com/Q/Are_all_odd_numbers_prime_numbers

No. 2 is even, but it's a prime number, and not a composite number. http://answers.yahoo.com/question/index?qid=20091012175114AAN2ikf

4. 1. A Prime Number can be divided evenly only by 1, or itself and it must be a whole number greater than 1. (www.mathsisfun.com/definitions/prime-number.html)

2. A Composite Number can be divided evenly by numbers other than 1 or itself. (http://www.mathsisfun.com/definitions/composite-number.html)

3. Not all odd numbers are prime numbers, eg. 9, 15, 21 can be divided by more than one number. (9 can be divided by 1, 3 and 9). (http://wiki.answers.com/Q/Are_all_odd_numbers_prime_numbers)

4. Not all even numbers are composite. Take 2 for example; its an even number but it only has 2 factors; 1 and itself. (http://wiki.answers.com/Q/Are_all_even_numbers_composite_why)

5. 1.A prime number is a number that is a whole number and have exactly 2 factors and that is the number 1 and the number itself.
2.Composite numbers are numbers that are whole numbers other than 1 and prime numbers ,composite numbers have more than 2 factors.(source: person longman maths insights express 1A)
3.No not all odd numbers are prime 9,27 have more than 2 factors 9: 1,3,9 27:1,3,9,27.so not all odd numbers are prime.
4.No not all even numbers are primes.2 has 2 factors so it is a prime number,not a composite number

6. 1.A prime number is a number that can be divided by 1 and itself.
2.A composite number have more than only two factors.
3.No,21 can be divided by 7and 3, 15 can be divided by 5 and 3.
4.No,Two only can be divided by itself and one.

7. 1. A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime because only 1 and 5 divide it, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6.
http://en.wikipedia.org/wiki/Prime_number
2. A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number.
http://en.wikipedia.org/wiki/Composite_number
3. Not all odd numbers are prime. E.g. the number 49 is odd, but it is not a prime.
4. Not all even numbers are composite. The number 2 is an even number, but it is not a composite.

8. 1. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.or example,

2. A natural number greater than 1 that is not a prime number is called a composite number. Ex. (6 is composite because it has the divisors 2 and 3 in addition to 1 and 6.)

Source : http://en.wikipedia.org/wiki/Prime_number

3. Not all odd numbers are prime numbers, eg. 9, 15, 21 can be divided by more than one number.

Source : http://wiki.answers.com/Q/Are_all_odd_numbers_prime_numbers

4.No. A composite number has factors in addition to one and itself while 2 has only 2 factors, 1 and itself.

9. 1. A prime number is an integer that cannot be factorized into other integers but is only divisible by itself or 1, such as 2, 3, 5, 7, and 11.
2. A composite number is an integer that can be divided by at least two other integer besides itself and 1 without leaving a remainder.
3. Not all odd numbers are prime. For instance, 9, 21, and 27 are multiples of 3 and though they are odd, they are not prime numbers.
4. No, 2 is the only even number that is prime as it can be divided by 1 and itself.
(http://www.thefreedictionary.com/composite+number)

10. 1.A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.
2. A natural number greater than 1 that is not a prime number is called a composite number
3.no, because some odd numbers can be divided by another number other than 1 and itself.
4. no because 2 is an even number and it is a prime, though the rest are composites.

1. http://en.wikipedia.org/wiki/Prime_numbers

11. 1:A positive integer that is not divisible without remainder by any integer except itself and 1, with 1 often excluded
2:A number that is a multiple of at least two whole numbers other than itself and 1.
3:No, some odd numbers can still be divided by a number other than itself and 1, e.g. 9 (9/3=3)
4:No, the only non-composite number which is larger than 1, an even number but not able to be divided by at least two whole numbers other than itself and 1, is 2. The factor of 2 is 2 and 1, therefore 2 is a prime and not a composite number.

Source:http://dictionary.reference.com/

12. A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number.

(Source: http://en.wikipedia.org/wiki/Prime_number,http://en.wikipedia.org/wiki/Composite_number)

13. 3. A prime number is a number that can only be divided by 1 or by itself. Not all odd numbers are prime numbers, eg. 9, 15, 21 can be divided by more than one number.

4. No. 2 is prime. All the rest are divisible by 2,so they are composite.

14. 1. an integer that has no integral factors but itself and 1. (wordnetweb.princeton.edu/perl/webwn)
2. A Composite Number can be divided evenly by numbers other than 1 or itself. (http://www.mathsisfun.com/definitions/composite- number.html)
3. No. 9 is an odd number but it is not a prime number.
4. No. 2 is an even number but it is not a composite number.

15. 1. A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.
2. A natural number greater than 1 that is not a prime number is called a composite number.
(1&2= http://en.wikipedia.org/wiki/Prime_number )
3. No, some odd numbers may be multiples of other numbers.
4. No, 2 is not a composite number because it can be divided by only 1 and itself.

16. 1. A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime because only 1 and 5 divide it, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. The uniqueness in this theorem requires excluding 1 as a prime because it is the multiplicative identity.
2. composite number is a positive integer that has at least one positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number.
(http://en.wikipedia.org/wiki/)
3. No. 9 is an odd number but it is not a prime number.
4. No, 2 is not a composite number because it can be divided by only 1 and itself.

17. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. (e.g. 2, 3, 5, 7, 13...)

A composite number is a positive integer that has at least one positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number. ( e.g. 4, 6, 8, 9, 10...)

Source: Wikipedia