Article Divisibility Rules: Is Number Divisible by 2,3,4,5,6,7,8,9

Discussion in 'Quantitative Aptitude' started by shabbir, Dec 1, 2013.

  1. shabbir

    shabbir Administrator Staff Member

    Divisibility Rule for 2

    Number ending with 0,2,4,6, or 8 are divisible by 2. These are also known as Even numbers.

    Divisibility Rule for 3

    A number is divisible by 3 if the sum of its digits is divisible by 3.

    36 Sum of digit is 3+6 = 9 is divisible by 3 and so 36 is divisible by 3.

    Not if you have a very large number then you can apply the same rule multiple times to determine the divisibility.

    As an example 222369963222222369555963 sum of digits is 2+2+2+3+6+9+9+6+3+2+2+2+2+2+2+3+6+9+5+5+5+9+6+3 = 105 = 1+5 = 6 which is divisible by 3 and so 222369963222222369555963 is divisible by 3.

    Divisibility Rule for 4

    A number is divisible by 4 if it’s last two digits are divisible by 4.

    Divisibility Rule for 5

    A number is divisible by 5 if the its last digit is either 0 or 5.

    Divisibility Rule for 6

    A number is divisible by 6 if its ending with 0,2,4,6, or 8 and its sum of digit are divisible by 3. In short if a number is divisible by 2 and 3 both, then number is divisible by 6.

    Divisibility Rule for 7

    There are many divisibility rules for 7 and for some small 3 or 4 digit we can use the following rule.

    Double the last digit and subtract it from the rest of the number. The answer is either 0 or a number divisible by 7.

    609 – 9×2 = 18. 60-18 = 42 which is divisible by 7 and so 609 is divisible by 7.

    6846 – 6×2 = 12. 684-12 = 672.

    Again apply the same rule on 672.

    672 – 2×2 = 4. 67-4 63 which is divisible by 4 and so 6846 is divisible by 7.

    The above method is not very quick when the numbers is large. There are many other faster rules for divisibility by 7 and you can check out one of them here.

    Divisibility Rule for 8

    A number is divisible by 8 if its last three digits are divisible by 8

    Divisibility Rule for 9

    A number is divisible by 9 if the sum of its digits is divisible 9.

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