🔢 Divisibility Rules
1 exam question type, fully solvedA divisibility rule is a quick test that tells you whether one number divides another, just by looking at the digits — no long division needed. Memorising these turns a slow sum into a five-second glance.
• By 2: the last digit is even (0, 2, 4, 6, 8).
• By 5: the last digit is 0 or 5. By 10: the last digit is 0.
• By 4: the last two digits form a multiple of 4. By 8: the last three digits form a multiple of 8.
• By 3: the digit sum is a multiple of 3. By 9: the digit sum is a multiple of 9.
• By 6: divisible by both 2 and 3 together.
• By 11: the difference (sum of digits at odd places) − (sum at even places) is 0 or a multiple of 11.
• By 7 (the standard trick): chop off the last digit, double it, and subtract it from the rest; repeat until you reach a small number — if that is a multiple of 7, so is the original. For : , and 63 is , so 672 is divisible by 7.
For a composite divisor (like 12, 33 or 132), split it into co-prime factors and apply each rule — more on that in the “Many Divisors” topic.
5736 ends in 36, and , so 5736 is divisible by .
The digit sum of 4752 is , a multiple of 9, so 4752 is divisible by .
Q1Which of these is divisible by 4?
Q2Which of these is divisible by 9?
Q3A number ends in 0. It is definitely divisible by:
Real exam questions — Divisibility Rules
1 question types · 5 solved examples from real SSC papersEach divisor has a quick digit test, so you never actually divide. Run the easiest rule first to knock out wrong options.
Which of the following is divisible by 4: 7421, 5736, 8913, 3718?
Which of the following is divisible by 5 but NOT by 2: 6135, 7200, 3750, 4820?
What is the sum of the digits of 4752, and is 4752 divisible by 9?
How many of these are divisible by 10: 430, 725, 980, 1005, 1200?
The sum of the three-digit numbers abc, bca and cab is always divisible by which number: 35, 31, 41 or 37?