Number System
CSAT number system for UPSC Prelims Paper II — divisibility rules, factors, HCF and LCM, remainders, unit digits, trailing zeros and orders of magnitude.
SyllabusCSAT · Basic numeracy (numbers and their relations, orders of magnitude) — Class X level
The number system is the foundation of CSAT’s basic-numeracy questions. UPSC rarely asks advanced theory; it asks Class X ideas in clever packaging — “how many numbers between 100 and 500 are divisible by 7?”, “when will three bells ring together again?”, “what is the unit digit of a large power?”. Each has a one-line method, and each method also speeds up percentages, time-and-work and data-interpretation questions.
This is a Prelims-only chapter. With one-third negative marking, a quick and certain method matters more than raw calculation speed.
What this chapter covers
| Sub-topic | Typical CSAT question |
|---|---|
| Divisibility rules | Which of these numbers is divisible by 11? Find the missing digit |
| Factors | How many factors does 720 have? |
| HCF and LCM | When do lights change together? Largest number leaving the same remainder |
| Remainders and unit digits | Remainder of $2^{31} \div 5$; unit digit of $7^{95}$ |
| Factorials | Trailing zeros in $100!$ |
| Orders of magnitude | Lakh, crore, million, billion conversions |
Start with Number System: Divisibility, HCF–LCM and Remainders, then revise with the quick-revision sheet and test yourself on the practice set.