So, the working principle will be different now. But this time, our osculator is not negative (as in case of 7). That means all the “forget nine” adds to a number which is multiple of 9. For example: digit-sum of 135792_ 1 plus 3 plus 5 is 9, forget it. What did you do earlier (in the 1st chapter)? “Forget nine”. Recall the method for calculation of digit-sum. If it is divisible by 4 thenĢ) Check whether the number is divisible by 3 or not.ġ35792:92 is divisible by 4 and also (l+3+5+7+9+2=)27 is divisible by 3 hence the number is divisible by 12. If it is not divisible by 4, the number is not divisible by 12. If the sums of digits at odd and even places are equal or differ by a number divisible by 11, then the number is also divisible by 11.ģ245682: S 1 = 3 + 4 + 6 + 2= 15 and S 2 = 2 + 5 + 8 = 15Īs S 1 = S2 2 the number is divisible by 11.Ģ83712: S 1 = 2 + 3 + 1= 6 and S 2 = 8 + 7 + 2 = 17.Īs S 1 and S 2 differ by 11 (divisible by 11), the number is also divisible by 11.Ĩ4927291658: S 1 = 8+9+7+9+6+8=47and S 2=4+2+2+1+5=14Īs (S 1 – S 2 =) 33 is divisible by 11, the number is also divisible by 11.Īny number which is divisible by both 4 and 3, is also divisible by 12.ġ) First divide the last two-digit number by 4. If the sum of all the digits of a number is divisible by 9, the number is also divisible by 9.ģ9681: 3 + 9 + 6 + 8 + 1 =27 is divisible by 9, hence the number is also divisible by 9.Ĥ56138: 4 + 5 + 6 + 1 + 3 + 8= 27 is divisible by 9, hence the number is also divisible by 9.Īny number which ends with zero is divisible by 10. The same rule is applicable to check the divisibility by 125. Also, if the last three digits of a number are zeros, the number is divisible by 8.ġ256: As 256 are divisible by 8, the number is also divisible by 8.ġ35923120: As 120 is divisible by 8, the number is also divisible by 8.ġ39287000: As the number has three zeros at the end, the number is divisible by 8. If the last three digits of a number is divisible by 8, the number is also divisible by 8. The above calculations can be done in one line or even mentally. Whenever you find a number which looks divisible by 7, you may stop there and conclude the result without any hesitation.Ģ. ![]() ![]() In all the examples, each of the numbers obtained after the equal sign (=) is also divisible by 7. This and only this digit is used to check the divisibility of any number by 7. Once again, for your convenience, as 7 x 3 = 21 (one more than 2 x 10), our negative osculator is 2. (3) Can you get any osculator for an even number or a number ending with ‘5’? (No But why?)įirst of all we recall the osculator for 7.
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