The fastest divisibility checks on the GMAT rely on digit rules. A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8); by 5 if its last digit is 0 or 5; by 4 if its last two digits form a multiple of 4 (such as 1532 because 32 ÷ 4 = 8); by 8 if its last three digits form a multiple of 8; by 25 if its last two digits are 00, 25, 50, or 75; and by 125 if its last three digits are one of 000, 125, 250, 375, 500, 625, 750, or 875.
Composite divisibility conditions combine the prime tests. A number is divisible by 6 if it is both even and divisible by 3; by 12 if it is divisible by both 3 and 4; and by 15 if it ends in 0 or 5 and has a digit sum divisible by 3. A common trap is assuming that divisibility by both 4 and 6 forces divisibility by 24, but in fact LCM(4, 6) = 12 is the correct threshold.
For 3, 9, 11, and 7 the digit tests are less obvious but extremely useful. A number is divisible by 3 or 9 exactly when its digit sum is divisible by 3 or 9 respectively; thus 1458 with digit sum 1+4+5+8 = 18 is divisible by 9 (and 3 and 2). For 11 the alternating sum of digits, positive at odd positions and negative at even, must be a multiple of 11, so 143 has alternating sum 1 − 4 + 3 = 0, confirming 143 = 11 × 13. The 7-test doubles the last digit and subtracts from the rest: 105 becomes 10 − (2·5) = 0, so 105 is divisible by 7, and 203 becomes 20 − 6 = 14, also divisible by 7.