Factors and Multiples for CUET UG GAT 2026: Concepts, Tricks, Formulas, and MCQs with Solutions
Introduction to Factors and Multiples for CUET UG 2026
Factors and Multiples is one of the most fundamental topics in Quantitative Aptitude for CUET UG GAT 2026. Almost every arithmetic topic such as LCM, HCF, Fractions, Ratio, and Number System depends on a strong understanding of factors and multiples.
In CUET, students often get 1–3 direct or indirect questions from this topic. Mastering it can significantly improve speed and accuracy in the exam.
What is Factors and Multiples?
Factors
A factor of a number is a number that divides the given number exactly without leaving a remainder.
Example:
Factors of 12
1, 2, 3, 4, 6, 12
Multiples
A multiple of a number is the result obtained when the number is multiplied by an integer.
Example:
Multiples of 5
5, 10, 15, 20, 25
Important Formulas for Factors and Multiples
Number of Factors Formula:
If
n = p^a × q^b × r^c
Then
Number of factors =
(a + 1)(b + 1)(c + 1)
Sum of Factors Formula:
Sum of factors =
(1 + p + p² + … + p^a)
×
(1 + q + q² + … + q^b)
Short Tricks to Solve Factors and Multiples Questions
Trick 1: Even and Odd Rule
- Even numbers have factor 2
- Odd numbers never have factor 2
Trick 2: Divisibility by 9
Add digits
If sum divisible by 9 → number divisible by 9
Example
729
7 + 2 + 9 = 18
Divisible by 9
So 729 divisible by 9
Trick 3: Number of Factors Shortcut
Prime factorization first
Then add 1 to powers
Multiply results
Example
72
72 = 2³ × 3²
Number of factors
(3 + 1)(2 + 1)
= 4 × 3
= 12
Trick 4: Largest Factor of a Number
Largest factor (except itself)
= Number ÷ Smallest prime factor
Common Patterns of Questions in CUET UG GAT
Most repeated question types:
- Number of factors
- Highest common factor
- Lowest common multiple
- Divisibility rules
- Missing factor problems
- Smallest or largest multiple
- Remainder based questions
- Prime factorization problems
Why Factors and Multiples Topic is Important for CUET UG GAT 2026
- Direct questions appear every year
- Foundation of Number System
- Required for LCM and HCF
- Improves calculation speed
- High scoring topic
- Helps in other arithmetic chapters
- Easy to master with practice
Exam-oriented important MCQs on Factors and Multiples With Step-by-Step Solutions:
Q 4545) Neha distributes 24 pencils equally among students. In how many different ways can the pencils be distributed?
A. 8
B. 9
C. 10
D. 11
Answer: A. 8
Formula Used:
Number of factors=(a+1)(b+1)\text{Number of factors} = (a+1)(b+1)
Solution:
24 = 2³ × 3¹
Number of factors
= (3+1)(1+1)
= 4 × 2
= 8
Q 4546) Two bells ring every 10 minutes and 15 minutes respectively. After how many minutes will they ring together again?
A. 20
B. 25
C. 30
D. 35
Answer: C. 30
Formula Used:
LCM=pmax(a1,a2)×qmax(b1,b2)\text{LCM} = p^{\max(a_1,a_2)} \times q^{\max(b_1,b_2)}
Solution:
10 = 2 × 5
15 = 3 × 5
LCM
= 2 × 3 × 5
= 30
Q 4547) There are 36 oranges and 48 bananas. They must be packed into identical boxes so that each box contains the same number of fruits. What is the greatest number of fruits per box?
A. 10
B. 12
C. 14
D. 16
Answer: B. 12
Formula Used:
HCF=pmin(a1,a2)×qmin(b1,b2)\text{HCF} = p^{\min(a_1,a_2)} \times q^{\min(b_1,b_2)}
Solution:
36 = 2² × 3²
48 = 2⁴ × 3
HCF
= 2² × 3
= 12
Q 4548) Find the smallest number divisible by 4, 6, and 8.
A. 12
B. 24
C. 36
D. 48
Answer: B. 24
Formula Used:
LCM=pmax(a1,a2)×qmax(b1,b2)\text{LCM} = p^{\max(a_1,a_2)} \times q^{\max(b_1,b_2)}
Solution:
4 = 2²
6 = 2 × 3
8 = 2³
LCM
= 2³ × 3
= 24
Q 4549) A number leaves remainder 2 when divided by 5. What will be the remainder when divided by 10?
A. 4
B. 5
C. 6
D. 7
Answer: D. 7
Formula Used:
Number form
Number = divisor × quotient + remainder
Solution:
Number form
5k + 2
Take smallest value
5 × 1 + 2
= 7
7 ÷ 10
Remainder
= 7
Q 4550) How many multiples of 7 are there between 1 and 70?
A. 8
B. 10
C. 11
D. 12
Answer: B. 10
Formula Used:
Number of multiples
= Last number ÷ divisor
Solution:
70 ÷ 7
= 10
Q 4551) Find the greatest number that divides 54 and 90 leaving remainder 0.
A. 12
B. 14
C. 16
D. 18
Answer: D. 18
Formula Used:
HCF=pmin(a1,a2)×qmin(b1,b2)\text{HCF} = p^{\min(a_1,a_2)} \times q^{\min(b_1,b_2)}
Solution:
54 = 2 × 3³
90 = 2 × 3² × 5
HCF
= 2 × 3²
= 18
Q 4552) A number has prime factorization 2² × 3¹ × 5¹. How many factors does the number have?
A. 9
B. 10
C. 11
D. 12
Answer: D. 12
Formula Used:
Number of factors=(a+1)(b+1)(c+1)\text{Number of factors} = (a+1)(b+1)(c+1)
Solution:
(2+1)(1+1)(1+1)
= 3 × 2 × 2
= 12
Q 4553) Find the smallest multiple of 9 greater than 80.
A. 71
B. 79
C. 81
D. 84
Answer: C. 81
Formula Used:
n×(⌊xn⌋+1)n \times \left(\left\lfloor \frac{x}{n} \right\rfloor + 1\right)
Solution:
80 ÷ 9
= 8 remainder
Next multiple
9 × 9
= 81
Q 4554) Find the greatest multiple of 8 less than 100.
A. 92
B. 94
C. 96
D. 98
Answer: C. 96
Formula Used:
n×⌊xn⌋n \times \left\lfloor \frac{x}{n} \right\rfloor
Solution:
100 ÷ 8
= 12
8 × 12
= 96
Q 4555) A number is divisible by 3, 5, and 6. What is the smallest such number?
A. 25
B. 28
C. 30
D. 32
Answer: C. 30
Formula Used: LCM
Solution:
3 = 3
5 = 5
6 = 2 × 3
LCM
= 2 × 3 × 5
= 30
Q 4556) The product of two numbers is 180 and their HCF is 6. Find their LCM.
A. 23
B. 25
C. 28
D. 30
Answer: D. 30
Formula Used:
HCF×LCM=Product of two numbers\text{HCF} \times \text{LCM} = \text{Product of two numbers}
Solution:
6 × LCM = 180
LCM
= 180 ÷ 6
= 30
Q 4557) How many factors does 81 have?
A. 5
B. 6
C. 7
D. 8
Answer: A. 5
Formula Used: Number of factors
Solution:
81 = 3⁴
Number of factors
4 + 1
= 5
Q 4558) A rectangular floor of 24 m and 36 m is to be tiled with square tiles. Find the largest tile size.
A. 10 m
B. 12 m
C. 14 m
D. 16 m
Answer: B. 12
Formula Used: HCF
Solution:
24 = 2³ × 3
36 = 2² × 3²
HCF
= 2² × 3
= 12
Q 4559) How many multiples of 5 are there between 1 and 100?
A. 13
B. 15
C. 18
D. 20
Answer: D. 20
Formula Used:
Number of multiples
= Last number ÷ divisor
Solution:
100 ÷ 5
= 20
FAQs on Factors and Multiples for CUET UG 2026
Q1: Is Factors and Multiples important for CUET UG GAT?
Yes. It is a foundational topic and appears directly or indirectly in many questions.
Q2: How many questions come from this topic in CUET?
Usually
1 to 3 questions
Q3: What is the fastest way to solve factor questions?
Use
Prime factorization method
Q4: Is this topic easy to score in CUET?
Yes. With practice, it becomes one of the highest scoring topics.
Q5: Which topics depend on Factors and Multiples?
- LCM and HCF
- Fractions
- Ratio and Proportion
- Number System
- Simplification
Conclusion
Factors and Multiples is one of the most important and scoring topics for CUET UG GAT 2026. A strong understanding of this topic improves speed, accuracy, and confidence in solving arithmetic problems.
By practicing the MCQs, learning the short tricks, and understanding the patterns, students can easily secure marks from this section in the exam.
Consistent practice of this topic will also make advanced topics like LCM, HCF, and Number System much easier to master.
Related Links
LCM and HCF for CUET UG GAT 2026 – Formulas, Tricks, Questions, and Solutions
Ratio and Proportion Questions for CUET UG GAT 2026 – Formulas, Tricks, MCQs with Solutions
Number System Mock Test for CUET UG GAT 2026: MCQs with Answers (CUET Pattern)
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About the Author
Vimal Kumar Tulsyan is the Founder of CUET NOW, an educational platform focused on CUET UG preparation. He has more than 10 years of teaching experience in Reasoning and General Aptitude.
His mission is to make CUET preparation simple, reliable, and accessible for every student.
