Number System Questions for SSC GD

Types of Numbers

Numbers are classified into different types. Natural numbers start from 1 (counting numbers). Whole numbers include 0 also. Integers include negative numbers too. Rational numbers can be written as p/q (like 3/4). Irrational numbers cannot (like root 2, pi). Prime numbers have exactly two factors: 1 and itself. Composite numbers have more than two factors.

• Natural Numbers: 1, 2, 3, 4 ... (no zero, no negative)
• Whole Numbers: 0, 1, 2, 3 ... (zero included)
• Integers: ...-2, -1, 0, 1, 2... (negatives included)
• Prime Numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 (first 15 primes — memorize these)
• 1 is neither prime nor composite — this is a direct exam trap
• 2 is the only even prime number

Divisibility Rules

Divisibility rules let you quickly find if a number is divisible by another without doing full division. SSC GD asks these directly — a number is given and you pick which divisors apply. Learn the rule for each number 2 to 11 and you can answer in under 10 seconds.

• Div by 2: Last digit is 0, 2, 4, 6, or 8
• 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 8: Last three digits divisible by 8
• Div by 9: Sum of all digits divisible by 9
• Div by 10: Last digit is 0
• Div by 11: Difference of (sum of odd-position digits) and (sum of even-position digits) is 0 or divisible by 11

Unit Digit (Last Digit) Calculation

SSC GD often asks: what is the unit digit of a big power like 7 to the power 55? You do not calculate the full number. Unit digits follow a cycle (pattern). Find which position in the cycle the power falls at, and you have the answer in 15 seconds.

• Unit digit of powers of 2: cycle is 2, 4, 8, 6 (repeats every 4)
• Unit digit of powers of 3: cycle is 3, 9, 7, 1 (repeats every 4)
• Unit digit of powers of 7: cycle is 7, 9, 3, 1 (repeats every 4)
• Unit digit of powers of 8: cycle is 8, 4, 2, 6 (repeats every 4)
• Unit digit of powers of 1, 5, 6: always 1, 5, 6 respectively (no cycle needed)
• Unit digit of powers of 4: odd power gives 4, even power gives 6
• Unit digit of powers of 9: odd power gives 9, even power gives 1

Factors and Number of Factors

A factor of a number divides it exactly. SSC GD asks how many factors a number has, or asks to find the sum of factors. The standard method is to do prime factorization first, then apply the formula.

• To find total factors: Write number as (p^a) x (q^b) x (r^c)..., then total factors = (a+1)(b+1)(c+1)
• Example: 12 = 2^2 x 3^1, so factors = (2+1)(1+1) = 6
• Perfect numbers: sum of all factors (excluding itself) equals the number. Example: 6 (factors 1,2,3 add to 6)
• A perfect square always has an odd number of total factors
• Prime number has exactly 2 factors: 1 and itself

Remainder and Dividend-Divisor Relationship

A standard formula connects dividend, divisor, quotient and remainder. SSC GD gives you three of these values and asks for the fourth. This is a direct formula application — memorize it and you solve in under 20 seconds.

• Dividend = Divisor x Quotient + Remainder
• Remainder is always less than Divisor
• If remainder = 0, the number is perfectly divisible
• When a number is divided by 10, remainder = unit digit of that number

• Thinking 1 is a prime number — it is NOT. 1 is neither prime nor composite. This appears directly in MCQs.
• In unit digit cycle, when remainder is 0 after dividing power by 4, many pick the first item in the cycle instead of the last (4th). Always take the last item when remainder is 0.
• Confusing divisibility by 4 rule with divisibility by 2 rule — divisibility by 4 needs LAST TWO digits, not just last one.
• In the factors formula, forgetting to add 1 to each exponent. Writing (a)(b)(c) instead of (a+1)(b+1)(c+1).
• Assuming all even numbers are divisible by 4 — for example 10 is even but not divisible by 4.

• DIVISIBILITY HOOK for 3 and 9: Both use digit sum. If digit sum divisible by 3, number divisible by 3. If divisible by 9, same rule with 9. Think 3-9 are brothers, they share the digit sum trick.
• UNIT DIGIT CYCLE for 2,3,7,8 all repeat every 4. Just remember the four cycles: 2(2,4,8,6), 3(3,9,7,1), 7(7,9,3,1), 8(8,4,2,6). Notice 3 and 7 cycles are reverses of each other.
• FACTOR FORMULA memory: PRIME-POWER-PLUS-ONE. Take prime powers, add one to each, multiply all together.
• For 4 and 9 unit digits, think ODD-EVEN: odd power keeps base digit, even power gives the other (4 gives 6, 9 gives 1).

• SSC GD typically places 2-3 questions from Number System in the quantitative section. Expect one on divisibility, one on unit digit, and one on dividend-divisor relationship.
• Unit digit questions are the most repeated pattern in recent SSC GD papers. Practice at least 15 such questions before exam. They can be solved in under 20 seconds each.
• Questions on prime numbers often disguise themselves as general knowledge-style questions: Which of the following is prime? Know all primes up to 50.
• Divisibility by 11 is a favourite trap question. Practice the odd-even position method on at least 5 examples.
• Do not spend more than 40 seconds on any Number System question. If you know the rule, it is fast. If you are calculating fully, you are doing it wrong — go back to the rule.