, Number System
1. Divisibility Rules
Think of divisibility like shortcuts to see if a number is “friendly” with another number.
● Ends with 0,2,4,6,8 → divisible by 2
● Sum of digits divisible by 3 → divisible by 3
● Last 2 digits divisible by 4 → divisible by 4
● Ends with 0 or 5 → divisible by 5
● Divisible by both 2 and 3 → divisible by 6
● Last 3 digits divisible by 8 → divisible by 8
● Sum of digits divisible by 9 → divisible by 9
● (Sum of odd place digits – sum of even place digits) divisible by 11 → divisible by 11
👉 These tricks save your seconds in exams.
2. LCM & HCF
● HCF = greatest number that divides both.
● LCM = smallest number that comes in both tables.
Formula:
LCM×HCF=Product of two numbersLCM \times HCF = Product \, of \, two \,
numbersLCM×HCF=Productoftwonumbers
3. Even & Odd Numbers
They behave like friends:
● Even + Even = Even
● Odd + Odd = Even
1. Divisibility Rules
Think of divisibility like shortcuts to see if a number is “friendly” with another number.
● Ends with 0,2,4,6,8 → divisible by 2
● Sum of digits divisible by 3 → divisible by 3
● Last 2 digits divisible by 4 → divisible by 4
● Ends with 0 or 5 → divisible by 5
● Divisible by both 2 and 3 → divisible by 6
● Last 3 digits divisible by 8 → divisible by 8
● Sum of digits divisible by 9 → divisible by 9
● (Sum of odd place digits – sum of even place digits) divisible by 11 → divisible by 11
👉 These tricks save your seconds in exams.
2. LCM & HCF
● HCF = greatest number that divides both.
● LCM = smallest number that comes in both tables.
Formula:
LCM×HCF=Product of two numbersLCM \times HCF = Product \, of \, two \,
numbersLCM×HCF=Productoftwonumbers
3. Even & Odd Numbers
They behave like friends:
● Even + Even = Even
● Odd + Odd = Even
