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Aptitude Topics

Factors & Multiples

Factors and multiples form the foundation of number systems. Understanding them helps solve divisibility, HCF, LCM, remainder, and arithmetic problems quickly.

Fundamental Principles

Factor

A factor of a number is a number that divides it exactly without leaving any remainder.

Multiple

A multiple of a number is obtained by multiplying it by whole numbers.

Prime Factor

A prime factor is a factor that is itself a prime number.

Essential Formulation Tips

  • Every number has at least two factors: 1 and itself.
  • 1 is a factor of every natural number.
  • Every number is a multiple of itself.
  • Factors are finite, but multiples are infinite.
  • Prime factorization helps solve many aptitude problems.

Shortcut Execution Techniques

  • If a number ends in 0, 2, 4, 6, or 8, it is divisible by 2.
  • If the sum of digits is divisible by 3, the number is divisible by 3.
  • If the last two digits are divisible by 4, the number is divisible by 4.
  • If a number ends in 0 or 5, it is divisible by 5.
  • Use factor pairs to quickly count total factors.

Contextual Inquiries (FAQs)

Q: What is the difference between a factor and a multiple?

A: Factors divide a number exactly, while multiples are obtained by multiplying the number.

Q: Can a number have infinite factors?

A: No. Every number has a finite number of factors.

Q: Are multiples infinite?

A: Yes. A number has infinitely many multiples.