Number System

Learning Objectives

• Understand the fundamental concepts of Number System
• Apply key formulas and techniques to solve problems
• Practice with exam-level questions to build speed and accuracy

Key Concepts

Number System for SSC GD & Agniveer

The number system forms the foundation of arithmetic. For SSC GD and Agniveer exams, questions cover types of numbers, LCM & HCF, divisibility rules, unit digits, and basic number theory at the 10th standard level. This topic is essential for the mathematics section of both exams.

Key Concepts

Types of Numbers: Natural (1,2,3...), Whole (0,1,2...), Integers (...-2,-1,0,1,2...), Prime (2,3,5,7,11...), Composite (4,6,8,9,10...), Co-prime (numbers with HCF 1, e.g., 4 and 9). Divisibility Rules: 2 (last digit even), 3 (sum of digits divisible by 3), 4 (last 2 digits divisible by 4), 5 (ends in 0/5), 6 (divisible by both 2 and 3), 7 (double last digit, subtract from rest, repeat), 8 (last 3 digits divisible by 8), 9 (sum of digits divisible by 9), 10 (ends in 0), 11 (difference of sum of odd-even place digits is 0 or multiple of 11). LCM & HCF: LCM is the smallest common multiple of numbers. HCF is the greatest common divisor. For two numbers: Product = LCM × HCF. For fractions: LCM = LCM of numerators / HCF of denominators; HCF = HCF of numerators / LCM of denominators. Unit Digit Cyclicity: Unit digit of powers repeats every 4 for digits 2,3,7,8 and every 2 for 4,9. Cyclicity: 2→2,4,8,6; 3→3,9,7,1; 4→4,6; 7→7,9,3,1; 8→8,4,2,6; 9→9,1.

Solved Examples