Number System: Complete Guide

Divisibility Rules

Key Rules to Memorize

• 2: Last digit even
• 3: Sum of digits divisible by 3
• 4: Last two digits divisible by 4
• 5: Last digit 0 or 5
• 6: Divisible by both 2 and 3
• 8: Last three digits divisible by 8
• 9: Sum of digits divisible by 9
• 11: Difference of alternate digit sums divisible by 11

HCF and LCM

• HCF × LCM = Product of two numbers
• For fractions: HCF = HCF of numerators / LCM of denominators

Prime Numbers

• First 20 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71
• Number of primes less than 100: 25

Remainder Theorems

• (a + b) mod n = [(a mod n) + (b mod n)] mod n
• (a × b) mod n = [(a mod n) × (b mod n)] mod n

Practice Tip

Master divisibility rules first - they save 30-40 seconds per question.