Number System Questions for RRB GROUP D

Types of Numbers

Numbers are classified into different types and RRB often asks you to identify whether a number belongs to a particular type. Natural numbers start from 1, whole numbers from 0, integers include negatives too. Prime numbers have exactly two factors: 1 and themselves. Composite numbers have more than two factors. 1 is neither prime nor composite — this is a top trick question.

• Natural Numbers: 1, 2, 3, 4... (no zero, no negatives)
• Whole Numbers: 0, 1, 2, 3... (zero included)
• Integers: ...-2, -1, 0, 1, 2... (negatives included)
• Prime Numbers: exactly 2 factors — 1 and itself (2 is the only even prime)
• Composite Numbers: more than 2 factors (4, 6, 8, 9...)
• 1 is NEITHER prime NOR composite — most common trap in RRB

Divisibility Rules

Divisibility rules are tested directly in RRB Group D. You are given a large number and asked which divisor it is divisible by. Memorise rules for 2 through 11. The rule for 11 is the trickiest but appears often. Divisible by 11 means: difference between sum of digits at odd places and sum of digits at even places is 0 or divisible by 11.

• Div by 2: last digit is even
• Div by 3: sum of all digits divisible by 3
• Div by 4: last two digits divisible by 4
• Div by 5: last digit is 0 or 5
• Div by 6: divisible by both 2 and 3
• Div by 9: sum of all digits divisible by 9
• Div by 11: (sum of odd-place digits) minus (sum of even-place digits) = 0 or multiple of 11

LCM and HCF

LCM (Lowest Common Multiple) is the smallest number divisible by all given numbers. HCF (Highest Common Factor) is the largest number that divides all given numbers. RRB Group D frequently gives word problems like: bells ringing at intervals, tiles fitting a floor, or distributing items equally. Key relationship to remember: LCM x HCF = Product of the two numbers (only valid for exactly TWO numbers).

• HCF divides all given numbers; LCM is divisible by all given numbers
• LCM x HCF = Product of two numbers (two numbers ONLY)
• For fractions: HCF = HCF of numerators / LCM of denominators
• For fractions: LCM = LCM of numerators / HCF of denominators
• HCF is always less than or equal to the smallest number
• LCM is always greater than or equal to the largest number

Remainders and Unit Digits

Remainder questions ask what is left when a large number is divided by another. Unit digit questions ask for the last digit of a big power like 7 raised to 55. For unit digits, the trick is that every number's unit digit repeats in a cycle. You just find the power modulo the cycle length. For example, 7 has a cycle of 4: 7,9,3,1 then repeats. So 7 to the power 55: 55 divided by 4 gives remainder 3, so unit digit is 3rd in cycle = 3.

• Unit digit of powers of 2 repeats in cycle of 4: 2,4,8,6
• Unit digit of powers of 3 repeats in cycle of 4: 3,9,7,1
• Unit digit of powers of 7 repeats in cycle of 4: 7,9,3,1
• Unit digit of powers of 4: cycle of 2 — 4,6,4,6
• Unit digit of powers of 5: always 5. Powers of 6: always 6
• For remainders: use the rule (a+b) mod n = [(a mod n) + (b mod n)] mod n

Factors and Multiples

Number of factors of a number is found by prime factorisation. If a number N = p raised to a times q raised to b, then total factors = (a+1)(b+1). RRB sometimes asks how many factors a number has, or asks for the sum of factors. Perfect numbers (like 6 and 28) where sum of proper divisors equals the number itself also appear occasionally.

• Total factors of N = p^a x q^b is (a+1)(b+1)
• To find factors: do prime factorisation first
• Number of even factors = total factors minus odd factors
• Odd factors: ignore all powers of 2, use remaining prime factorisation
• Perfect number: 6 (factors: 1,2,3 sum to 6) and 28 are standard examples

• Saying 1 is a prime number — 1 is NEITHER prime nor composite. Costs 1 mark every time.
• Applying LCM x HCF = Product formula to THREE numbers — this formula is valid for exactly two numbers only.
• In unit digit cycle, if the remainder comes out as 0, taking the 0th term instead of the LAST term of the cycle. e.g. 2 to power 8: 8 mod 4 = 0, unit digit is 4th term = 6, not the 0th.
• Confusing HCF of fractions and LCM of fractions — mixing up numerator and denominator rules for the two.
• In divisibility by 11, counting digit positions from left instead of consistently applying odd/even place rule from right to left.

• MNEMONIC for divisibility: 2-Even last, 3-Sum, 4-Last two, 5-Zero or Five, 6-Both 2 and 3, 9-Sum again, 11-Odd minus Even. Phrase: Every Student Loves To Study Hard — E=Even, S=Sum, L=Last two, T=Two/Five, S=Sum, H=Hard(11).
• For unit digit cycles, think of 4 soldiers standing in a circle for 2,3,7,8 (cycle of 4). Only 4 and 9 are lazy — cycle of 2. 5 and 6 are frozen — always same.
• LCM is Large (always bigger or equal to numbers). HCF is Humble (always smaller or equal). L for Large, H for Humble.
• For HCF of fractions: H goes TOP to TOP and BOTTOM gets LCM. For LCM of fractions: L goes TOP to TOP and BOTTOM gets HCF. Think: both formulas use the numerator normally but the denominator swaps the operation.

• RRB Group D typically has 2-3 LCM/HCF word problems per paper — bells ringing together and sharing items equally are the two most common formats. Practice these quickly.
• Unit digit questions appear almost every year. They look intimidating with big powers but take only 20-30 seconds once you know cycles. Easy 1 mark — never skip.
• Divisibility rule questions are straightforward fill-in type. A 5-6 digit number is given and you pick the correct divisor. Expect 1-2 such questions — solve in under 30 seconds.
• Factor counting questions (how many factors does X have) appear 1-2 times. Always do prime factorisation as first step — no shortcut around it.
• Avoid spending more than 90 seconds on any Number System question. If a remainder problem looks complex, try small values or elimination — RRB options are usually well-spaced and you can back-calculate.