Divisibility, HCF & LCM Tricks and Formulas

Divisibility Tests

  • A number is divisible by 2, if its unit’s place digit is 0, 2, 4, or 8

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

  • A number is divisible by 4, if the number for med by its last two digits is divisible by 4

  • A number is divisible by 8, if the number formed by its last three digits is divisible by 8

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

  • A number is divisible by 11, if, starting from the RHS, (Sum of its digits at the odd place) – (Sum of its digits at even place) is equal to 0 or 11x

HCF and LCM

Productoftwonumbers=TheirH.C.F.×TheirL.C.M.

Application of H.C.F.

The greatest natural number that will divide x, y and z leaving remainders r1, r2 and r3, respectively, is the H.C.F.of(xr1),(yr2)and(zr3)

Application of L.C.M.

The smallest natural number that is divisible by x, y and z leaving the same remainder r in each case is the L.C.M.of(x,yandz)+r

H.C.F. and L.C.M. of Fractions

H.C.F.offractions=H.C.F.ofnumberatorsofallfractionsH.C.M.ofdenominatorsofallfractions

L.C.M.offractions=L.C.M.ofnumberatorsofallfractionsH.C.F.ofdenominatorsofallfractions