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    Prime Number

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    hb749856
    The document discusses several key concepts: 1) It defines prime numbers as natural numbers only divisible by 1 and themselves, and lists the first few prime numbers. 2) It explains two methods for identifying prime numbers - using the rule of 6n±1, and checking if a number is divisible by 5 or 7. 3) It describes divisibility rules for several numbers, including rules for checking if a number is divisible by 7 and 11 based on the digits. 4) It provides a table outlining divisibility rules for numbers 2 through 10.

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    Prime Number

    Uploaded by

    hb749856
    10 views3 pages
    The document discusses several key concepts: 1) It defines prime numbers as natural numbers only divisible by 1 and themselves, and lists the first few prime numbers. 2) It explains two methods for identifying prime numbers - using the rule of 6n±1, and checking if a number is divisible by 5 or 7. 3) It describes divisibility rules for several numbers, including rules for checking if a number is divisible by 7 and 11 based on the digits. 4) It provides a table outlining divisibility rules for numbers 2 through 10.

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    The document discusses several key concepts: 1) It defines prime numbers as natural numbers only divisible by 1 and themselves, and lists the first few prime numbers. 2) It explains two methods for identifying prime numbers - using the rule of 6n±1, and checking if a number is divisible by 5 or 7. 3) It describes divisibility rules for several numbers, including rules for checking if a number is divisible by 7 and 11 based on the digits. 4) It provides a table outlining divisibility rules for numbers 2 through 10.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    10 views3 pages

    Prime Number

    Uploaded by

    hb749856
    The document discusses several key concepts: 1) It defines prime numbers as natural numbers only divisible by 1 and themselves, and lists the first few prime numbers. 2) It explains two methods for identifying prime numbers - using the rule of 6n±1, and checking if a number is divisible by 5 or 7. 3) It describes divisibility rules for several numbers, including rules for checking if a number is divisible by 7 and 11 based on the digits. 4) It provides a table outlining divisibility rules for numbers 2 through 10.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 3

    What is Prime Number .

    Prime Number are natural number that are divisible by only 1 and the number itself.
    The first few prime numbers are;
    2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97.

     The largest known prime number is 282,589,933-1 which has 24,862,048 digits.
     The smallest prime number is 2
     The only even prime number is 2
     No prime number ends in 0,2,4,6,8

    How Can identify Prime Number .

    We can identify prime number by the rule of 6n±1.


    It states that;
    All prime number greater than 3 can be expressede in the form 6n±1, where n is a natural
    number and the number is not be divisble by 5 or 7.
    For Example;
    The number 11,13,17,19,23 is prime number that can all expressed as 6n±1;
    11=6(2) – 1
    13=6(2) + 1
    17=6(3) - 1
    19=6(3) +1
    23=6(4) - 1

    Again;
    If we see that the number 25 which can be expressed as;

    6n ± 1
    =6(4) +1
    =25
    But it is not prime number because it can be divisible by 5. (5×5=25).
    What is the Divisibility Rule of 7?
    The divisibility rule of 7 states that, a number is divisible by 7, if “the difference between
    twice the unit digit of the given number and the remaining part of the given number
    should be a multiple of 7 or it should be equal to 0”.

    For example, 798 is divisible by 7.

    Explanation:

    The unit digit of 798 is 8.

    If the unit digit is doubled, we get 16 (i.e., 8 x 2 = 16)

    The remaining part of the given number is 79.

    Now, take the difference between 79 and 16.

    = 79-16

    =63

    Here, the difference value obtained is 63, which is a multiple of 7. (i.e., 9 x 7 = 63)

    Thus, the given number 798 is divisible by 7.

    What is the Divisibility Rule of 11?

    The divisibility rule of 11 states that, a number is divisible by 11, if


    the difference of the sum of alternative digits of a number is divisible by 11, then that
    number is divisible by 11 completely.

    i.e., Sum of digits in odd places – Sum of digits in even places = 0 or a multiple of 11

    In order to check whether a number like 2143 is divisible by 11, below is the following
    procedure.

     Group the alternative digits i.e., digits which are in odd places together and digits in
    even places together. Here 24 and 13 are two groups.
     Take the sum of the digits of each group i.e., 2+4=6 and 1+3= 4
     Now find the difference of the sums; 6-4=2
     If the difference is divisible by 11, then the original number is also divisible by 11.
    Here 2 is the difference which is not divisible by 11.
     Therefore, 2143 is not divisible by 11.
    Number Law
    2 If a number is even or a number whose last digit is an
    even number i.e. 2,4,6,8 including 0, it is always
    completely divisible by 2.
    3 Divisibility rule for 3 states that a number is completely
    divisible by 3 if the sum of its digits is divisible by 3.
    4 If the last two digits of a number are divisible by 4,
    then that number is a multiple of 4 and is divisible by 4
    completely.
    5 Numbers, which last with digits, 0 or 5 are always
    divisible by 5.
    6 Numbers which are divisible by both 2 and 3 are
    divisible by 6. That is, if the last digit of the given
    number is even and the sum of its digits is a multiple of
    3, then the given number is also a multiple of 6.
    8 If the last three digits of a number are divisible by 8,
    then the number is completely divisible by 8.
    9 The rule for divisibility by 9 is similar to divisibility
    rule for 3. That is, if the sum of digits of the number is
    divisible by 9, then the number itself is divisible by 9.
    10 Divisibility rule for 10 states that any number whose
    last digit is 0, is divisible by 10.

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