Divisibility Rules for 1,2,3,4,5,6,7,8,9,10,11,12,13
Divisibility Rules
Divisibility Rules are rules or tests using which you can quickly determine if a particular number is divisible by some other number without performing actual division.
For example, if you want to know if a particular number is divisible by 4 then you can use divisibility rules for 4.
Divisibility Rules for 1
Every integer is divisible by 1 and quotient is always number itself.
Ex. 23 ÷ 1 = 23
484 ÷ 1 = 484
473 ÷ 1 = 473
Divisibility Rules For 2
A Number is divisible by 2 If it has Any of the Digits 0,2,4,6,8 in it’s unit Place.
Ex. 1348373642, 38374, 9447390, 274838.
All of these Number is divisible by 2 because in the unit place of these have 2,4,0,8 digits.
You can repeat this process when needed.
Divisibility Rules For 3
If the sum of the digits of number is divisible by 3 then the number is divisible by 3.
Ex. 219 = 2+1+9 = 12÷3 = 4
4893 = 4+8+9+3 = 24 ÷ 3 = 8
1932 = 1+9+3+2 = 15÷3 = 5
All of these number’s digit sum is divisible by 3 then whole number is divisible by 3.
Divisibility Rules For 4
A number with 3 or more digit is divisible 4 if the formed by it’s last two digits is divisible by 4. Divisibility for 1 & 2 digit number by 4 has to be calculate by actual division.
Ex. 1922 = last 2 digit sum = 2+2 = 4÷ 4 = 1
2048 = last 2 digit sum = 4+8 = 12 ÷ 4 = 3
So these number last two digit sum is divisible by 4 so these number also divisible by 4.
Divisibility Rules For 5
A number which has either 0 or 5 in its units place is divisible by 5.
Ex. 6325 , 6300 , 383375, 4837375, 12525645
We can see these Number have 0 & 5 in in their unit Place so these are divisible by 5 .
Divisibility Rules For 6
If a number is divisible by both 2 & 3 then it’s divisible by 6 also.
Ex. 1932, 297144, 1790184, 639210 is divisible by 2 & 3, so it’s also divisible by 6.
Divisibility Rules For 7
• Multiply the digit in the unit place by 2 and subtract it from the rest. if the last remaining number is divisible by 7 then the original number is also divisible by 7. Apply this rule till needed.
Ex. 679 = unit digit 9×2= 18
= 67-18 = 49
49 is divisible by 7 so whole number is divisible by 7.
• Multiply the number in the unit place by 5 and add it to the the rest . if the last remaining number is divisible by 7 then original number is divisible by 7.
Ex. 4823 = unit digit = 3×5 = 15
= 482+15 = 497
497 = 7×5 = 35
= 49+35 = 84
84 is divisible by 7 so whole number is divisible by 7.
Divisibility Rules For 8
A number with 4 or more digit is divisible by 8, if the number formed by last three digit is divisible by 8.
Ex. 74512 = last 3 digit 512÷8 = 64
2856 = last 3 digit 856÷8 = 107
Last three digit is divisible by 8 so whole number is divisible by 8.
Divisibility Rules For 9
If the sum of the digit of number is divisible by 9 then the number itself is divisible by 9.
Ex. 63612 = sum of digits
= 6+3+6+1+2= 18÷9 = 2 429714 = sum of digits
= 4+2+9+7+1+4= 27÷9 =3
Sum of digits is divisible by 9 so these number are divisible by 9.
Divisibility Rules For 10
If a number has 0 in the last place of then it’s divisible by 10.
Ex. 47484740, 3636360, 236630, 347830 All these have 0 in unit place so they are divisible by 10.
Divisibility Rules For 11
Find the difference between the sum of Digit at odd places ( from the right) and sum of Digit at Even Places (from right ) of the Number. If the difference is either 0 or divisible by 11 then the number is divisible by 11.
Ex. 61809 = odd place sum = 9+8+6 = 23
Even places sum = 0+1 = 1
Difference = 23-1 = 22÷11 = 2
Difference divisible by 11 so this number also divisible by 11.
Divisibility Rules For 12
If a number is divisible by 4 & 3 both then number is divisible by 12.
Ex. 4536 is divisible by 3 & 4 both so it is divisible by 12 also.
Divisibility Rules For 13
Multiply last digit from 9 and subtract it form rest number. If result is divisible by 13 or 0 then whole number is divisible by 13.
Ex. 5642 = last digit 2 × 9 = 18
= 564 – 18 = 546
= 546
= 54 – 6×9 = 0
Results is 0 so it’s divisible by 13.
Here given all most useful divisibility rules. Hope you like it. Thank you
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