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.
Example Breakdown: Finding Factors
Basic factor identification.1 × 24 = 24
2 × 12 = 24
3 × 8 = 24
4 × 6 = 24
Factors = {1, 2, 3, 4, 6, 8, 12, 24}
Example Breakdown: Finding Multiples
Simple multiples concept.7 × 1 = 7
7 × 2 = 14
7 × 3 = 21
7 × 4 = 28
7 × 5 = 35
Example Breakdown: Prime Factorization
Important for HCF and LCM.60 = 2 × 30
30 = 2 × 15
15 = 3 × 5
Prime factors = 2² × 3 × 5
Set 1: Basics of Factors
Understanding what makes a factor.
Q1. Which of these is a factor of 10?
Q2. Is 1 a factor of every number?
Q3. Which is NOT a factor of 12?
Q4. Are factors always smaller than or equal to the number?
Q5. How many factors does 7 have?
Q6. Is 4 a factor of 8?
Q7. Which is the largest factor of 15?
Q8. Is 2 a factor of 9?
Q9. Which of these is a factor of 20?
Q10. Does 6 have more than two factors?