General Importance

  • Divisibility rules help quickly check if a number can be divided by another without remainder.
  • These rules are essential for solving questions on HCF, LCM, factors, multiples, and simplification.
  • Frequently asked in SSC CGL, CHSL, RRB NTPC, Banking exams.

Rule for Divisibility by 2

  • A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.
  • Examples: 34, 78, 120.
  • All even numbers are divisible by 2.

Rule for Divisibility by 3

  • A number is divisible by 3 if the sum of its digits is divisible by 3.
  • Example: 123 (1+2+3=6; 6 divisible by 3).
  • Applicable to any size of number.

Rule for Divisibility by 4

  • A number is divisible by 4 if the last two digits form a number divisible by 4.
  • Example: 312 (12 divisible by 4).
  • All multiples of 100 are divisible by 4 (since 100 ends with 00).

Rule for Divisibility by 5

  • A number is divisible by 5 if its last digit is 0 or 5.
  • Examples: 25, 70, 105.
  • Very useful for quickly identifying multiples of 5.

Rule for Divisibility by 6

  • A number is divisible by 6 if it is divisible by both 2 and 3.
  • Example: 72 is divisible by 2 (even) and by 3 (sum=9).
  • Check 2 and 3 rules to confirm divisibility by 6.

Rule for Divisibility by 7

  • Double the last digit, subtract it from the remaining number; if result is divisible by 7, the original number is too.
  • Example: 203 (double 3=6; 20−6=14; 14 divisible by 7).
  • Can be repeated if necessary for large numbers.

Rule for Divisibility by 8

  • A number is divisible by 8 if its last three digits form a number divisible by 8.
  • Example: 4,216 (216 divisible by 8).
  • Numbers ending in 000 are always divisible by 8.

Rule for Divisibility by 9

  • A number is divisible by 9 if the sum of its digits is divisible by 9.
  • Example: 729 (7+2+9=18; 18 divisible by 9).
  • Similar to the rule for 3 but checks divisibility by 9.

Rule for Divisibility by 10

  • A number is divisible by 10 if its last digit is 0.
  • Examples: 40, 130, 990.
  • All multiples of 10 end with zero.

Rule for Divisibility by 11

  • Find the difference between the sum of the digits in odd positions and even positions.
  • If the difference is 0 or divisible by 11, the number is divisible by 11.
  • Example: 121 (1+1=2; 2−2=0; divisible).
  • Another example: 2728 (2+2=4; 7+8=15; 15−4=11; divisible).

Miscellaneous Facts

  • Divisibility rules save time in calculations.
  • These rules are critical in HCF and LCM problems.
  • Help in quickly reducing fractions.
  • Are frequently tested in number series and missing number questions.

Category

Questions