Divisibility rules

key notes:

🔢 Divisibility by 2

  • A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.
    ✨ Example: 248 ➝ last digit 8 ✔️

🔢 Divisibility by 3

  • Add all the digits.
  • If the sum is divisible by 3, then the number is also divisible by 3.
    ✨ Example: 351 → 3+5+1 = 9 ✔️

🔢 Divisibility by 4

  • Look at the last two digits.
  • If those digits form a number divisible by 4, then the whole number is divisible by 4.
    ✨ Example: 524 → last two digits 24 ✔️

🔢 Divisibility by 5

  • A number is divisible by 5 if it ends in 0 or 5.
    ✨ Example: 775 ➝ ends in 5 ✔️

🔢 Divisibility by 6

  • A number is divisible by 6 if it is divisible by 2 AND 3.
    ✨ Example: 264 → even ✔️ and 2+6+4 = 12 (divisible by 3) ✔️

🔢 Divisibility by 8

  • Check the last three digits.
  • If they form a number divisible by 8, the whole number is divisible by 8.
    ✨ Example: 6,432 → last three digits 432 ✔️

🔢 Divisibility by 9

  • Add all digits.
  • If the sum is divisible by 9, the number is divisible by 9 too.
    ✨ Example: 4,131 → 4+1+3+1 = 9 ✔️

🔢 Divisibility by 10

  • A number is divisible by 10 if it ends in 0.
    ✨ Example: 840 → ends in 0 ✔️

🎯 Why Divisibility Rules Are Useful?

  • Helps in quick calculations
  • Makes factorization easier
  • Useful for finding LCM/GCD
  • Saves time during exams 🕒✨

Learn with an example

🗼 Type a digit that makes this statement true.

645,02 _____ is divisible by 2.

  • Yes
  • no

Since the number 645,02 ? is divisible by 2, the missing digit must be 0, 2, 4, 6, or 8.

🗼 Type a digit that makes this statement true.

50,515,51 _____ is divisible by 10.

  • yes
  • no

Since the number 50,515,51 ? is divisible by 10, the missing digit must be 0.

🗼Is 6,487,572 divisible by 10?

  • yes
  • no
  • Try the “divisible by 10” rule on 6,487,572.
  • Look at the ones digit:
  • 6,487,572
  • The ones digit is 2. 
    The rule says that 6,487,572 is not divisible by 10.

let’s practice: