Number System Questions for SSC CHSL

Types of Numbers

Numbers are classified based on their properties. Knowing the definitions quickly helps you answer classification and true/false type questions in SSC CHSL without wasting time.

• Natural Numbers: 1, 2, 3, ... (counting numbers, starts at 1)
• Whole Numbers: 0, 1, 2, 3, ... (natural numbers + zero)
• Integers: ...-2, -1, 0, 1, 2... (includes negatives)
• Rational Numbers: can be written as p/q where q is not zero (includes fractions, terminating decimals)
• Irrational Numbers: cannot be written as p/q — examples are root 2, root 3, pi
• Prime Numbers: exactly 2 factors — 1 and itself. Note: 1 is NOT prime, 2 is the only even prime

Divisibility Rules

SSC CHSL directly asks which number is divisible by 4, 8, 11, etc. Memorise these rules cold — they save time and prevent silly errors. Divisibility by 7 is rarely tested so skip it.

• Div by 2: last digit even
• Div by 3: sum of digits divisible by 3
• Div by 4: last two digits divisible by 4
• Div by 8: last three digits divisible by 8
• Div by 9: sum of digits divisible by 9
• Div by 11: (sum of digits at odd positions) minus (sum of digits at even positions) = 0 or divisible by 11

HCF and LCM

Highest Common Factor (HCF) is the largest number that divides both numbers. Lowest Common Multiple (LCM) is the smallest number divisible by both. These are tested in word problems about bells ringing together, cutting ropes, tiling floors, etc.

• For two numbers: HCF x LCM = Product of the two numbers
• HCF is always less than or equal to the smaller number
• LCM is always greater than or equal to the larger number
• Fractions: HCF of fractions = HCF of numerators / LCM of denominators
• Fractions: LCM of fractions = LCM of numerators / HCF of denominators

Remainder and Divisibility Tricks

Remainder questions are a favourite in SSC CHSL. The most common pattern: a number leaves remainder R when divided by D — find remainder when divided by another number. Also tested: what value of x makes the expression divisible by a number.

• If N = D x Q + R, then R is the remainder (0 <= R < D)
• Remainder of (a + b) divided by n = (remainder of a + remainder of b) divided by n
• Remainder of (a x b) divided by n = (remainder of a x remainder of b) divided by n
• A number divisible by both 4 and 9 is also divisible by 36 (LCM of 4 and 9)

Unit Digit Problems

SSC CHSL regularly asks: what is the unit digit of a large power like 7^84 or 3^100? Unit digits of powers follow a cycle. Memorise the cycle lengths and you can solve in under 30 seconds.

• Digits 0, 1, 5, 6 always give the same unit digit regardless of power
• Digit 4: cycle is 4, 6 (odd power = 4, even power = 6)
• Digit 9: cycle is 9, 1 (odd power = 9, even power = 1)
• Digits 2, 3, 7, 8: cycle of 4 — divide the power by 4 and use the remainder
• Cycle for 2: 2, 4, 8, 6. Cycle for 3: 3, 9, 7, 1. Cycle for 7: 7, 9, 3, 1. Cycle for 8: 8, 4, 2, 6

Number of Factors

Questions asking how many factors (divisors) a number has are asked occasionally in SSC CHSL. The method uses prime factorisation.

• Step 1: Write the number as a product of prime factors — N = p^a x q^b x r^c
• Step 2: Number of factors = (a+1)(b+1)(c+1)
• Number of odd factors: ignore the power of 2 in the factorisation, apply formula to remaining primes
• A perfect square always has an odd number of factors

• Treating 1 as a prime number — it is NOT prime. 2 is the smallest and only even prime number.
• In HCF x LCM = a x b, this formula works ONLY for two numbers, not three or more numbers.
• In unit digit of powers, when the power is exactly divisible by 4 (remainder 0), many students pick the 0th term instead of the 4th term of the cycle.
• Confusing divisibility by 4 (check last two digits) with divisibility by 8 (check last three digits) — a common exam trap is to give a number like 1312 and ask divisibility by 8.
• In remainder problems, forgetting that remainder must be non-negative and less than the divisor — writing negative remainders is a mistake.

• WHOLE = NATURAL + ZERO. Think: a WHOLE roti includes the NATURAL ingredients plus the ZERO (the hole in a donut).
• For divisibility by 11, remember ODD minus EVEN = 0 or 11. Shortcut word: OMEO (Odd Minus Even is the Operation).
• Unit digit cycles of 2, 3, 7, 8 all repeat every 4 steps — remember the phrase FOUR IS THE FLOOR for these four digits.
• HCF x LCM = Product — think of it as a SEESAW: if HCF goes up, LCM must come down to keep the product balanced.

• SSC CHSL typically has 2 to 4 direct Number System questions per paper. Unit digit and divisibility questions appear almost every year — prioritise these two.
• HCF/LCM word problems are set in real-life contexts like traffic lights blinking, bells ringing, or workers completing tasks together — recognise the pattern and apply formula immediately.
• Remainder questions involving large powers (like 17^30 divided by 7) appear at moderate difficulty — practice the modular arithmetic trick of reducing the base first.
• Do not spend more than 45 seconds on any Number System question in the exam. If you are stuck on a remainder or factor question, skip and return — these are solvable but time-consuming if formula is forgotten.
• Negative marking is 0.5 marks in SSC CHSL. For divisibility questions you should be near 100 percent accurate since rules are fixed — never guess here.