Classify numbers with suitable examples, and explain the divisibility rules that help in quick calculation.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Open in two lines. A number system groups numbers by their properties. Knowing the groups and the divisibility rules lets you solve aptitude questions without long working.
2 · Draw the number tree. [Diagram: Real numbers → Rational (integers → whole numbers → natural numbers; fractions; ending or repeating decimals) and Irrational (√2, √3, π)]
3 · Natural numbers, whole numbers and integers. Natural: 1, 2, 3, … Whole: 0, 1, 2, … Integers: … −2, −1, 0, 1, 2, … Every natural number is whole, and every whole number is an integer.
4 · Rational and irrational numbers. Rational: p/q with q ≠ 0, e.g. 3/4, −5, 0.333… Irrational: cannot be written as p/q; the decimal never ends or repeats, e.g. √2, π.
5 · Even, odd, prime, composite and co-prime.
Even: divisible by 2 (0, 8, 36); odd: not divisible by 2 (7, 15).
Prime: exactly two factors (2, 3, 5, 7); 2 is the only even prime.
Composite: more than two factors (4, 9, 12); 1 is neither prime nor composite.
Co-primes: HCF is 1, e.g. 8 and 15.
6 · Divisibility rules with examples.
2: last digit even. 5: last digit 0 or 5. 10: last digit 0.
3 and 9: digit sum divisible by 3 or 9 (7,236 → 18).
4: last two digits divisible by 4 (7,316). 8: last three digits (21,416).
11: difference of alternate-digit sums is 0 or a multiple of 11 (9,284).
7 · Use in competitive exams. Missing-digit, unit-digit and remainder questions in bank, SSC and placement tests are solved in seconds with these rules.
8 · Close in one line. Classifying a number first and testing it with the rules saves time and avoids long division.
Scoring tip: Draw the number tree first; it earns marks on its own. Give one example for every type and every rule.
