✨ Factors, Multiples & Divisibility

Last Updated: 06-Sep-2025

What are Factors?

A factor of a number divides it exactly (no remainder).

👉 Example:

  • Factors of 12 → 1, 2, 3, 4, 6, 12

Hinglish Tip 🗣 : Factor = Number ko divide karne wale numbers.

What are Multiples?

A multiple of a number is found by multiplying it with 1, 2, 3, …

👉 Example:

  • Multiples of 4 → 4, 8, 12, 16, 20, …

Hinglish Tip 🗣 : Multiple = Number ko bar-bar jodna/multiply karna.

Divisibility

If one number divides another without remainder, then it is divisible.

👉 Example:

  • 18 ÷ 6 = 3 → Divisible ✅
  • 19 ÷ 6 = remainder 1 → Not divisible ❌

Odd & Even Numbers

Number is even if it is divisible by 2 and odd if it is not divisible by 2.

👉 Example:

  • Even → Divisible by 2 → 2, 4, 6, 8, …
  • Odd → Not divisible by 2 → 1, 3, 5, 7, …

Prime & Composite Numbers

  • Prime Number → Only 2 factors: 1 and itself.
    • Examples: 2, 3, 5, 7, 11 …
  • Composite Number → More than 2 factors.
    • Examples: 4, 6, 8, 9, 10 …

Hinglish Tip 🗣 : Prime = Sirf 1 aur khud se divide hota hai. Composite = Dusre numbers se bhi divide hota hai.

HCF (Highest Common Factor)

HCF = Biggest number that divides two or more numbers exactly.

👉 Example:

  • Factors of 12 → 1, 2, 3, 4, 6, 12
  • Factors of 18 → 1, 2, 3, 6, 9, 18
  • Common factors → 1, 2, 3, 6
  • HCF = 6

Hinglish Tip 🗣 : HCF = Sabse bada common factor.

LCM (Lowest Common Multiple)

LCM = Smallest number that is a multiple of both numbers.

👉 Example:

  • Multiples of 4 → 4, 8, 12, 16, 20 …
  • Multiples of 6 → 6, 12, 18, 24 …
  • Common multiples → 12, 24 …
  • LCM = 12

Hinglish Tip 🗣 : LCM = Sabse chhota common multiple.

Palindrome Numbers

A palindrome number reads the same forwards and backwards.

How to check (manually):

  1. Write the number.
  2. Read the digits from right to left.
  3. If the sequence is the same as left-to-right, it is a palindrome.

👉 Examples:

  • 121 → forward 121, backward 121 → palindrome.
  • 1331 → forward 1331, backward 1331 → palindrome.
  • 7 → single-digit numbers (0–9) are palindromes by default.
  • 123 → forward 123, backward 321 → not a palindrome.

Notes:

  • Some numbers can be both prime and palindromic (e.g., 131 is a palindromic prime).
  • Palindromes are useful in puzzles, coding tasks, and number pattern problems.

Hinglish Tip 🗣 : Palindrome = "Ulta padhne par bhi same" — jaise 121 ya 1331.

Other Special Number Types

  • Perfect Number: Equals sum of its proper divisors.
    • Example: 6 → 1 + 2 + 3 = 6.
  • Square Number: Product of an integer with itself.
    • Example: 1, 4, 9, 16, 25.
  • Triangular Number: Sum of first n natural numbers.
    • Example: 1, 3, 6, 10, 15.
  • Armstrong Number: Sum of its digits each raised to the power of count of digits equals the number.
    • Example: 153 → 1³ + 5³ + 3³ = 153.

⚡ Quick Practice

  1. List all factors of 30.
  2. First 5 multiples of 11.
  3. Find HCF of 18 and 24.
  4. Find LCM of 9 and 12.
  5. Is 1221 a palindrome? (Show how you checked.)
  6. Is 131 both prime and palindrome?
  7. Identify if 28 is a perfect number.
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